Please define the coefficient of thermal expansion?

Answer:

Molar mass of the gas will be 60.65 gram/mole

Explanation:

We have given mass of gas = 3.7 gram

Gas contains [tex]3.7\times 10^{22}[/tex]

We know that any gas contain [tex]6.022\times 10^{23}[/tex] molecules in 1 mole

So number of moles [tex]=\frac{3.7\times 10^{22}}{6.022\times 10^{23}}=0.061[/tex]

We know that number of moles [tex]n=\frac{mass\ in\ gram}{molar\ mass}[/tex]

So [tex]0.061=\frac{3.7}{molar\ mass}[/tex]

Molar mass = 60.65 gram/mole

The rate of heat transfer through the skier's clothing is approximately 230.4 watts.

Given the information you provided, we can calculate the rate of heat transfer through the skier's clothing using the following formula for heat conduction:

Q = k * A * ΔT / L

where:

Q is the heat transfer rate (W)

k is the thermal conductivity of the clothing (W/m K)

A is the body surface area (m²)

ΔT is the temperature difference between the skin and the outer surface of the clothing (K)

L is the thickness of the clothing (m)

Let's plug in the values:

k = 0.040 W/m K

A = 1.80 m²

ΔT = 33.0°C - 1.0°C = 32.0 K (convert temperature difference from Celsius to Kelvin)

L = 0.01 m (convert centimeter to meter)

Q = 0.040 W/m K * 1.80 m² * 32.0 K / 0.01 m

Q = 230.40 W

Answer:

a)No, I wouldn't.

b) It can be improved through alloys.

Explanation:

Iron is a metal with lower resistance to corrosion, this means it will show visible signs of oxidation in living tissue, this corrosion happens so rapidly that supply and migration of oxygen can't pace with the consumption of the oxidant so that the contact tissue becomes starving of oxygen, this is the reason why I wouldn't use pure iron as an implant material.

Iron can be used in alloys to improve its properties, reducing the corrosion, but keeping the iron's resistance for implants in places with higher mechanical stress, one example is Iron-Chromium-Nickel alloys.

I hope you find this information useful! Good luck!

Answer:

Initial temperature = 170. 414 °C

Total mass = 94.478 Kg

Final volumen = 33.1181 m^3

Diagram  = see picture.

Explanation:

We can consider this system as a close system, because there is not information about any output or input of water, so the mass in the system is constant.  

The information tells us that the system is in equilibrium with two phases: liquid and steam. When a system is a two phases region (equilibrium) the temperature and pressure keep constant until the change is completed (either condensation or evaporation). Since we know that we are in a two-phase region and we know the pressure of the system, we can check the thermodynamics tables to know the temperature, because there is a unique temperature in which with this pressure (800 kPa) the system can be in two-phases region (reach the equilibrium condition).  

For water in equilibrium at 800 kPa the temperature of saturation is 170.414 °C which is the initial temperature of the system.  

to calculate the total mass of the system, we need to estimate the mass of steam and liquid water and add them. To get these values we use the specific volume for both, liquid and steam for the initial condition. We can get them from the thermodynamics tables.

For the condition of 800 kPa and 170.414 °C using the thermodynamics tables we get:

Vg (Specific Volume of Saturated Steam) = 0.240328 m^3/kg

Vf (Specific Volume of Saturated Liquid) = 0.00111479 m^3/kg

if you divide the volume of liquid and steam provided in the statement by the specific volume of saturated liquid and steam, we can obtain the value of mass of vapor and liquid in the system.

Steam mass = *0.9 m^3 / 0.240328 m^3/kg = 3.74488 Kg

Liquid mass = 0.1 m^3 /0.00111479 m^3/kg = 89.70299 Kg  

Total mass of the system = 3.74488 Kg + 89.70299 Kg = 93,4478 Kg

If we keep the pressure constant increasing the temperature the system will experience a phase-change (see the diagram) going from two-phase region to superheated steam. When we check for properties for the condition of P= 800 kPa and T= 350°C we see that is in the region of superheated steam, so we don’t have liquid water in this condition.  

If we want to get the final volume of the water (steam) in the system, we need to get the specific volume for this condition from the thermodynamics tables.  

Specific Volume of Superheated Steam at 800 kPa and 350°C = 0.354411 m^3/kg

We already know that this a close system so the mass in it keeps constant during the process.

If we multiply the mass of the system by the specific volume in the final condition, we can get the final volume for the system.  

Final volume = 93.4478 Kg * 0.354411 m^3/kg = 33.1189 m^3

You can the P-v diagram for this system in the picture.  

For the initial condition you can calculate the quality of the steam (measure of the proportion of steam on the mixture) to see how far the point is from for the condition on all the mix is steam. Is a value between 0 and 1, where 0 is saturated liquid and 1 is saturated steam.  

Quality of steam = mass of steam / total mass of the system

Quality of steam = 3.74488 Kg /93.4478 Kg = 0,040 this value is usually present as a percentage so is 4%.  

Since this a low value we can say that we are very close the saturated liquid point in the diagram.  

The initial temperature of the water is 170.41 °C.

The initial volume of the water is 1 cubic meter.

The mass of the water is 4.620 kilograms.

The final volume of the water is 1.62828 cubic meters.

The process is described in the [tex]P-\nu[/tex] diagram attached below.

By steam tables we find the missing properties of water:

[tex]p = 800\,kPa[/tex], [tex]T = 170.41\,^{\circ}C[/tex], [tex]\nu = 0.21643\,\frac{m^{3}}{kg}[/tex], [tex]h = 2563.62\,\frac{kJ}{kg}[/tex] (Liquid-Vapor Mix) ([tex]x = 90\,\%[/tex])

[tex]p = 800\,kPa[/tex], [tex]T = 350\,^{\circ}C[/tex], [tex]\nu = 0.35442\,\frac{m^{3}}{kg}[/tex], [tex]h = 3162.2\,\frac{kJ}{kg}[/tex] (Superheated Vapor)

Now we proceed to calculate the initial temperature, initial volume, mass and the final volume of the water:

[tex]T_{1} = 170.41\,^{\circ}C[/tex]

The initial temperature of the water is 170.41 °C. [tex]\blacksquare[/tex]

[tex]V_{1} = 0.9\,m^{3}+0.1\,m^{3}[/tex]

[tex]V_{1} = 1\,m^{3}[/tex]

The initial volume of the water is 1 cubic meter. [tex]\blacksquare[/tex]

[tex]m = \frac{V_{1}}{\nu_{1}}[/tex] (1)

[tex]m = 4.620\,kg[/tex]

The mass of the water is 4.620 kilograms. [tex]\blacksquare[/tex]  

[tex]V_{2} = m\cdot \nu_{2}[/tex] (2)

[tex]V_{2} = 1.62828\,m^{3}[/tex]

The final volume of the water is 1.62828 cubic meters. [tex]\blacksquare[/tex]

The process is described in the [tex]P-\nu[/tex] diagram attached below. [tex]\blacksquare[/tex]

To learn more on piston-cylinder devices, we kindly invite to check this verified question: https://brainly.com/question/6334891

Answer:

Specific gravity is defined as the ratio of the Densities of the two substances.

Specific gravity = [tex]\frac{\textup{Density of substance}}{\textup{1000}}[/tex]

Explanation:

Specific gravity is defined as the ratio of the Densities of the two substances.

For the standardization, the density ration of densities is calculated with respect to the density of water i.e the denominator is the density of water.

Specific gravity = [tex]\frac{\textup{Density of substance}}{\textup{Density of water}}[/tex]

Also,

At STP density of water is 1000 Kg/m³

Therefore the relation between the specific gravity and density is,

The Specific gravity = [tex]\frac{\textup{Density of substance}}{\textup{Density of water at STP}}[/tex]

or

Specific gravity = [tex]\frac{\textup{Density of substance}}{\textup{1000}}[/tex]

Answer:

The cassette player will operate at normal power for 3333.33 seconds.

Explanation:

The first step is to identify the operating voltage and the operating current with the purpose to determine the power that the cassette player consumes. Remember that power equals the voltage multiplied by the current [tex]P=V\times I[/tex], where P is in Watts (W), V is in Volts (V) and I is in Amperes (A).

The problem says that four batteries are connected in series to provide a voltage of 6V to the player circuit. So, the operating voltage is 6V, [tex]V=6V[/tex]

Then, the problem says that cassette player draws a constant current of 10mA from the battery pack. So, the operating current is 10mA or 0.01A, [tex]I=0.01A[/tex]

From previous, it could be said that the cassette player consumes 0.06W.

[tex]P=V\times I=(6V)\times (0.01A)=0.06W[/tex]

Now, the idea is to calculate how long the cassette will operate at 0.06W.

The problem says that the battery pack stores [tex]200\, W\cdot s[/tex], it means that the battery pack could provide 200W in a second; after a second, the battery pack will not work properly. However, the battery pack just have to provide 0.06W so, it will last more time. For calculating that, you must divide the total power per time the cell can provide by the power that the cassette player needs to work.

[tex]t=\frac{200W\cdot s}{0.06W}=3333.33s[/tex]

As you can see, the W units are canceled and second remains.

Thus, the cassette player will operate at normal power for 3333.33 seconds.

Answer:

The heat transferred to water equals 1600 kJ

Explanation:

By the conservation of energy we have

All the kinetic energy of the moving vehicle is converted into thermal energy

We know that kinetic energy of a object of mass 'm' moving with a speed of 'v' is given by

[tex]K.E=\frac{1}{2}mv^{2}[/tex]

Thus

[tex]K.E_{car}=\frac{1}{2}\times 2000\times 40^{2}=1600\times 10^{3}Joules[/tex]

Thus the heat transferred to water equals [tex]1600kJ[/tex]

Explanation:

Step1

Gob is the primary element in the glass production.  Gob is the hot molten glass which can shape according to the shape of container.

Step2

Gob is filled in the mold in glass production. The shape of gob is different for different glass product in glass production process. So, the shape of gob is very important parameter for glass production. This gob is filled in the mold by guided method or the gravity method.

Answer:

overflow rate 20.53 m^3/d/m^2

Detention time 2.34 hr

weir loading  114.06 m^3/d/m

Explanation:

calculation for single clarifier

[tex]sewag\  flow Q = \frac{12900}{2} = 6450 m^2/d[/tex]

[tex]surface\  area =\frac{pi}{4}\times diameter ^2 = \frac{pi}{4}\times 20^2[/tex]

[tex]surface area = 314.16 m^2[/tex]

volume of tank[tex] V  = A\times side\ water\ depth[/tex]

                             [tex]=314.16\times 2 = 628.32m^3[/tex]

[tex]Length\ of\  weir = \pi \times diameter of weir[/tex]

                       [tex] = \pi \times 18 = 56.549 m[/tex]

overflow rate =[tex] v_o = \frac{flow}{surface\ area} = \frac{6450}{314.16} = 20.53 m^3/d/m^2[/tex]

Detention time[tex] t_d = \frac{volume}{flow} = \frac{628.32}{6450} \times 24 = 2.34 hr[/tex]

weir loading[tex]= \frac{flow}{weir\ length} = \frac{6450}{56.549} = 114.06 m^3/d/m[/tex]

Answer:

T=5.3° C

Explanation:

Given that

Power input to the pump = 2 KW

Building loses heat rate = 0.5 KW/C

So rate of heat transfer = 0.5(273+30-T)

rate of heat transfer = 0.5(303-T)

T=Ambient temperature

Building temperature = 30° C

We know that ,heat pump is used to heat the building.

COP of pump = 0.5 COP of Carnot heat pump

[tex]COP\ of\ Carnot\ heat\ pump=\dfrac{273+30}{303-T}[/tex]

[tex]COP\ of\ Carnot\ heat\ pump=\dfrac{303}{303-T}[/tex]

[tex]COP\ of\ pump=\dfrac{303-T}{Power}[/tex]    

[tex]COP\ of\ pump=0.5\times \dfrac{303-T}{2}[/tex]     -----1

And also

[tex]COP\ of\ pump=\dfrac{1}{2}\times \dfrac{303}{303-T}[/tex]   ----2

So from now equation 1 and 2

[tex]\dfrac{303-T}{4}=\dfrac{1}{2}\times \dfrac{303}{303-T}[/tex]

So T= 278.38 K=5.3° C

T=5.3° C

Ambient temperature =5.3° C.

Answer:

d = 2.69 mm

Explanation:

Assuming the cable is rated with a factor of safety of 1.

The stress on the cable is:

σ = P/A

Where

σ = normal stress

P: load

A: cross section

The section area of a circle is:

A = π/4 * d^2

Then:

σ = 4*P / (π*d^2)

Rearranging:

d^2 = 4*P / (π*σ)

[tex]d = \sqrt{4*P / (\pi*\sigma)}[/tex]

Replacing:

[tex]d = \sqrt{4*800 / (\pi*\90000)} = 0.106 inches[/tex]

0.106 inches = 2.69 mm

Answer:

The correct answer is option 'c': 13.8 kNm

Explanation:

We know that moment of a force equals

[tex]Moment=Force\times Arm[/tex]

The hydro static force is given by [tex]Force=Pressure\times Area[/tex]

We know that the hydrostatic pressure on a rectangular surface in vertical position is given by [tex]Pressure=\rho \times g\times h_{c.g}[/tex]

For the given rectangular surface we have [tex]h_{c.g}=\frac{h}{2}=\frac{1.5}{2}=0.75m[/tex]

Thus applying the values we get force as

[tex]Force=1000\times 9.81\times 0.75\times 1.5\times 2.5=27.59kN[/tex]

This pressure will act at center of pressure of the rectangular plate whose co-ordinates is given by h/3 from base

Thus applying the calculated values we get

[tex]Moment=27.59\times \frac{1.5}{3}=13.8kN.m[/tex]

Explanation:

The Challenger accident made them aware of the risks. They had been a little naive, since it was never believed that such a thing could happen. This, together with Space Shuttle Columbia disaster revealed the risks of the space shuttle program, which also had very high maintenance costs.

Answer:

The spring is compressed by 0.275 meters.

Explanation:

For equilibrium of the gas and the piston the pressure exerted by the gas on the piston should be equal to the sum of  weight of the piston and the force the spring exerts on the piston

Mathematically we can write

[tex]Force_{pressure}=Force_{spring}+Weight_{piston}[/tex]

we know that

[tex]Force_{pressure}=Pressure\times Area=300\times 10^{3}\times \frac{\pi \times 0.1^2}{4}=750\pi Newtons[/tex]

[tex]Weight_{piston}=mass\times g=100\times 9.81=981Newtons[/tex]

Now the force exerted by an spring compressed by a distance 'x' is given by [tex]Force_{spring}=k\cdot x=5\times 10^{3}\times x[/tex]

Using the above quatities in the above relation we get

[tex]5\times 10^{3}\times x+981=750\pi \\\\\therefore x=\frac{750\pi -981}{5\times 10^{3}}=0.275meters[/tex]

Answer:

Ek=207.569MJ

Ep=136.92MJ

Explanation:

kinetic energy is that energy that bodies with mass have when they have movement, while the potential energy is due to the height and mass that bodies have.

taking into account that the plane starts from rest at a height of zero, the following equations are taken to calculate the kinetic energy (Ek) and the potential energy (Ep)

[tex]Ek=0.5mv^{2} \\Ep=mgh[/tex]

where

m=mass=14000kg

v=speed=620km/h=172.2m/s

h=altitude=1000m

g=gravity=9.78 m/s^2

solving

Ek=(0.5)(14000)(172.2)^2=207569880J=207.569MJ

Ep=(14000)(9.78)(1000)=136920000=136.92MJ

Answer:

[tex]w = 8.316\times 10^6 lb[/tex]

Explanation:

force that structural base must be provided with is equal to the weight of water

we know that

[tex]\rho =\frac{mass}{V}[/tex]

[tex]m =\rho V[/tex]

We know that

w = mg

so we have

[tex]w = \rho Vg[/tex]

density of water  is 62.4 lb/ft^3

V = 1 milllion = 100,000 gallons

[tex]g = 32.1 ft/s^2[/tex]

[tex]w = 62.4[\times10^6 gallons \frac{0.134}{1 gallon}] [32.1 ft/s^2 \frac{0.3048 m/s^2}{ft/s^2} \frac{m/s^2}{9.8 m/s^2}][/tex]

[tex]w = 8.316\times 10^6 lb[/tex]

Answer:

Force on the car will be 4800 N and time required to cover this distance 13.75  sec

Explanation:

We have given mass of the car = 1200 kg

Initial velocity u = 20 km/h

Final velocity v = 75 km/h

Acceleration [tex]a=4m/sec^2[/tex]

From the first equation of motion we know that

v = u+at, here v is final velocity, u is initial velocity, a is acceleration and t is time

So [tex]75=20+4\times t[/tex]

t = 13.75 sec

From second law of motion we know that [tex]F=ma[/tex]

So force [tex]F=1200\times 4=4800N[/tex]

Answer:

1.53

Explanation:

Given:

depth of the unknown liquid  = 1.5m

the depth of the oil floating on top = 5m

specific weight of oil, γ = 8.5 kN/m³

Total pressure at the bottom = 65 kPa = 65 kN/m²

let the specific weight of the unknown liquid be " γ' "

Now,

The total pressure

= Pressure due to the unknown liquid + Pressure due to floating liquid

or

65 = γ' × 1.5 + γ × 5

or

65 = γ' × 1.5 + 8.5 × 5

or

22.5 = γ' × 1.5

or

γ' = 15 kN/m³

Also,

Specific gravity = [tex]\frac{\textup{Specific weight of unknown liquid}}{\textup{Specific weight of water}}[/tex]

specific weight of water = 9.81 kN/m³

or

Specific gravity = [tex]\frac{15}{\9.81}[/tex]  = 1.53

To calculate the specific gravity of the unknown liquid, you use the pressure reading from the tank, along with the height and specific weight of the oil, and then compare it to the specific weight of water.

The question revolves around finding the specific gravity of an unknown liquid using a pressure gauge reading at the bottom of a tank containing both oil and the unknown liquid. To find the specific gravity, we use the equation for pressure caused by a static fluid column, which is P = h⋅γ, where P is pressure, h is the height of the fluid column, and γ is the specific weight of the fluid. Based on the given pressure reading and the specific weight of the oil, we can determine the specific weight of the unknown liquid. Once we have that, the specific gravity is found by dividing the specific weight of the unknown liquid by the specific weight of water (9.81 kN/m3, since the specific weight of water is its density (1000 kg/m3) times the acceleration due to gravity (9.81 m/s2)).

The equation to find the specific gravity (SG) of the unknown liquid is SG = γunknown / γwater, where γunknown is the specific weight of the unknown liquid calculated from the pressure reading at the bottom of the tank, and γwater is the specific weight of water.

Answer:

Heat transferred from  the refrigerated space = 95.93 kJ/kg

Work required = 18.45 kJ/kg

Coefficient  of performance = 3.61

Quality at the beginning of the heat  addition cycle = 0.37

Explanation:

From figure  

[tex] Q_H [/tex] is heat rejection process

[tex] Q_L [/tex] is heat transferred from the refrigerated space

[tex] T_H [/tex] is high temperature = 50 °C + 273 = 323 K

[tex] T_L [/tex] is low temperature = -20 °C + 273 = 253 K  

[tex] W_{net} [/tex] is net work of the cycle (the difference between compressor's work and turbine's work)

Coefficient of performance of a Carnot refrigerator [tex] (COP_{ref}) [/tex] is calculated as

[tex] COP_{ref} = \frac{T_L}{T_H - T_L} [/tex]

[tex] COP_{ref} = \frac{253 K}{323 K - 253 K} [/tex]

[tex] COP_{ref} = 3.61 [/tex]

From figure it can be seen that heat rejection is latent heat of vaporisation of R-12 at 50 °C. From table

[tex] Q_H = 122.5 kJ/kg [/tex]

From coefficient of performance definition

[tex] COP_{ref} = \frac{Q_L}{Q_H - Q_L} [/tex]

[tex] Q_H \times COP_{ref} = (COP_{ref} + 1) \times Q_L[/tex]

[tex] Q_L = \frac{Q_H \times COP_{ref}}{(COP_{ref} + 1)} [/tex]

[tex] Q_L = \frac{122.5 kJ/kg \times 3.61}{(3.61 + 1)} [/tex]

[tex] Q_L = 95.93 kJ/kg [/tex]

Energy balance gives

[tex] W_{net} = Q_H - Q_L [/tex]

[tex] W_{net} = 122.5 kJ/kg - 95.93 kJ/kg [/tex]

[tex] W_{net} = 26.57 kJ/kg [/tex]

Vapor quality at the beginning of the heat addition cycle is calculated as (f and g refer to saturated liquid and saturated gas respectively)

[tex] x = \frac{s_1 - s_f}{s_g - s_f} [/tex]

From figure

[tex] s_1 = s_4 = 1.165 kJ/(K kg) [/tex]

Replacing with table values

[tex] x = \frac{1.165 kJ/(K \, kg) - 0.9305 kJ/(K \, kg)}{1.571 kJ/(K \, kg) - 0.9305 kJ/(K \, kg)} [/tex]

[tex] x = 0.37 [/tex]

Quality can be computed by other properties, for example, specific enthalpy. Rearrenging quality equation we get

[tex] h_1 = h_f + x \times (h_g - h_f) [/tex]

[tex] h_1 = 181.6 kJ/kg + 0.37 \times 162.1 kJ/kg [/tex]

[tex] h_1 = 241.58 kJ/kg [/tex]

By energy balance, [tex] W_{t} [/tex] turbine's work is

[tex] W_{t} = |h_1 - h_4| [/tex]

[tex] W_{t} = |241.58 kJ/kg - 249.7 kJ/kg| [/tex]

[tex] W_{t} = 8.12 kJ/kg [/tex]

Finally, [tex] W_{c} [/tex] compressor's work is

[tex] W_{c} = W_{net} + W_{t}[/tex]

[tex] W_{c} = 26.57 kJ/kg + 8.12 kJ/kg[/tex]

[tex] W_{c} = 34.69 kJ/kg [/tex]

Answer:

Basically there are two principal differences between the convection and conduction heat transfer

Explanation:

The conduction heat transfer is referred to the transfer between two solids due a temperature difference, while for, the convective heat transfer is referred to the transfer between a fluid (liquid or gas) and a solid. Also, they used different coefficients for its calculation.

We can include on the explanation that conduction thermal transfer is due to temperature difference, while convection thermal transfer is due to density difference.

Answer:

It falls at the same speed in both cases.

Explanation:

If I were standing still the phone would be in free fall after slipping out of my hand.

I set a frame of reference with origin on the ground and the positive Y axis pointing up.

It would slip at t0 = 0, from a position Y0 = 5 ft, with a speed of Vy0 = 0.

It would be subject to an gravitational acceleration of -32.2 ft/s^2.

Since acceleration is constant:

Y(t) = Y0 + Vy0 * t + 1/2 * 4 * t^2

When it hits the floor at t1 it will be at Y(t1) = 0

0 = 5 + 0 * t1 - 16.1 * t1^2

16.1 * t1^2 = 5

t1^2 = 5 / 16.1

[tex]t1 = \sqrt{0.31} = 0.55 s[/tex]

If the elevator is standing still it would take 0.55 s to hit the ground.

Now, if the elevator is moving up at 10 ft/s.

The frame of reference will have its origin at the place the floor of the elevator is at t = 0, and stay there as the elevetor moves. The floor of trhe elevator will have a position of Ye = 10 * t

Vy0 = 10 ft/s because it will be moving initially at the same speed as the elevator.

And it will hit the floor of the elevator not at 0, but at

Ye = 10 * t2

So:

10 * t2 = 5 + 10 * t2 - 16.1 * t2^2

0 = 5 - 16.1 * t2^2

16.1 * t1^2 = 5

t1^2 = 5 / 16.1

[tex]t1 = \sqrt{0.31} = 0.55 s[/tex]

It falls at the same speed in both cases.

Answer:

final temperature is 424.8 K

so correct option is e 424.8 K

Explanation:

given data

pressure p1 = 1 bar

pressure p2 = 5 bar

index k = 1.3

temperature t1 = 20°C = 293 k

to find out

final temperature  t2

solution

we have given compression is reversible and has an index k

so we can say temperature is

[tex]\frac{t2}{t1}= [\frac{p2}{p1}]^{\frac{k-1}{k} }[/tex]  ...........1

put here all these value and we get t2

[tex]\frac{t2}{293}= [\frac{5}{1}]^{\frac{1.3-1}{1.3} }[/tex]

t2 = 424.8

final temperature is 424.8 K

so correct option is e

Answer:

a)A constant volume process is called isochoric process.

b)Yes

c)Work =0

Explanation:

Isochoric process:

 A constant volume process is called isochoric process.

In constant volume process work done on the system or work done by the system will remain zero .Because we know that work done give as

work = PΔV

Where P is pressure and ΔV is the change in volume.

For constant volume process ΔV = 0⇒ Work =0

Yes heat transfer can be take place in isochoric process.Because we know that temperature difference leads to transfer of heat.

Given that

Initial P=10 MPa

Final pressure =15 MPa

Volume = 100 L

Here volume of gas is constant so the work work done will be zero.

Answer:

1st payment = $9350

4th payment = $9650

last 10th payment = $10250

Explanation:

given data

loan = $85000

time = 10 year

each payment larger = $100

time value of money = 10% per year

to find out

first, the fourth, and the last payment

solution

we find here actual value at end of 1st year that is

actual value = loan amount + 10% of loan

actual value N = 85000 + (10% ×85000 )

actual value N = $93500

so

1st payment is = [tex]\frac{actual value}{total time}[/tex]

1st payment is = [tex]\frac{93500}{10}[/tex]

1st payment = $9350

and

4th payment = 1st payment + 3× each payment larger

4th payment = 9350 + 3×100

4th payment = $9650

and

last 10th payment = 4th payment + 6× each payment larger

last 10th payment = 9650 + 6× 100

last 10th payment = $10250

Answer:

119.35 mm

Explanation:

Given:

Inside diameter, d = 100 mm

Tensile load, P = 400 kN

Stress = 120 MPa

let the outside diameter be 'D'

Now,

Stress is given as:

stress = Load × Area

also,

Area of hollow pipe = [tex]\frac{\pi}{4}(D^2-d^2)[/tex]

or

Area of hollow pipe = [tex]\frac{\pi}{4}(D^2-100^2)[/tex]

thus,

400 × 10³ N = 120 × [tex]\frac{\pi}{4}(D^2-100^2)[/tex]

or

D² = tex]\frac{400\times10^3+30\pi\times10^4}{30\pi}[/tex]

or

D = 119.35 mm

Answer:

D =119.35 mm

Explanation:

given data:

inside diameter = 100 mm

load = 400 kN

stress = 120MPa

we know that load is given as

[tex]P = \sigma A[/tex]  

where:

P=400kN = 400000N

[tex]\sigma = 120MPa[/tex]

[tex]A =(\frac{1}{4} \pi D^2 - \frac{1}{4}\pi (100^2)[/tex]

[tex]A=\frac{1}{4} \pi (D^2 - 10000)[/tex]

putting all value in the above equation to get the required diameter value

[tex]400 =  120*\frac{1}{4} \pi (D^2 - 10000)[/tex]

solving for

D =119.35 mm

Answer:

Torque at input shaft will be 176.8695 N-m

Explanation:

We have given input power [tex]P_{IN}=42.6KW=42.6\times 10^3W[/tex]

Angular speed = 2300 rpm

For converting rpm to rad/sec we have multiply with [tex]\frac{2\pi }{60}[/tex]

So [tex]2300rpm=\frac{2300\times 2\pi }{60}=240.855rad/sec[/tex]

We have to find torque

We know that  power is given by [tex]P=\tau \omega[/tex], here [tex]\tau[/tex] is torque and [tex]\omega[/tex] is angular speed

So [tex]42.6\times 10^3=\tau \times 240.855[/tex]

[tex]\tau =176.8695N-m[/tex]

So torque at input shaft will be 176.8695 N-m

Answer:

(a) dynamic viscosity = [tex]1.812\times 10^{-5}Pa-sec[/tex]

(b) kinematic viscosity = [tex]1.4732\times 10^{-5}m^2/sec[/tex]

Explanation:

We have given temperature T = 288.15 K

Density [tex]d=1.23kg/m^3[/tex]

According to Sutherland's Formula  dynamic viscosity is given by

[tex]{\mu} = {\mu}_0 \frac {T_0+C} {T + C} \left (\frac {T} {T_0} \right )^{3/2}[/tex], here

μ = dynamic viscosity in (Pa·s) at input temperature T,

[tex]\mu _0[/tex]= reference viscosity in(Pa·s) at reference temperature T0,

T = input temperature in kelvin,

[tex]T_0[/tex] = reference temperature in kelvin,

C = Sutherland's constant for the gaseous material in question here C =120

[tex]\mu _0=4\pi \times 10^{-7}[/tex]

[tex]T_0[/tex] = 291.15

[tex]\mu =4\pi \times 10^{-7}\times \frac{291.15+120}{285.15+120}\times \left ( \frac{288.15}{291.15} \right )^{\frac{3}{2}}=1.812\times 10^{-5}Pa-s[/tex]when T = 288.15 K

For kinematic viscosity :

[tex]\nu = \frac {\mu} {\rho}[/tex]

[tex]kinemic\ viscosity=\frac{1.812\times 10^{-5}}{1.23}=1.4732\times 10^{-5}m^2/sec[/tex]

Answer:

Engine not possible

Explanation:

source temperature T1 = 300 K

sink temperature T2= 283 K

therefore, carnot efficiency of the heat engine

η= 1- T_2/T_1

[tex]\eta= 1-\frac{T_1}{T_2}[/tex]

[tex]\eta= 1-\frac{283}{300}[/tex]

= 0.0566

= 5.66%

claims of work produce W = 100 kW,  mass flow rate = 20 kg/s

[tex]Q=mc_p(T_1-T_2)[/tex]

[tex]Q=20\times4.18(300-283)[/tex]

= 1421.2 kW

now [tex]\eta= \frac{W}Q}[/tex]

now [tex]\eta= \frac{100}{1421.2}[/tex]

=7%

clearly, efficiency is greater than carnot efficiency hence the engine is not possible.

Answer:

Total work: -5.25 kJ

Total Heat: 52 kJ

Explanation:

V0 = 0.15

P0 = 350 kPa

t0 = 150 C = 423 K

P1 = 105 kPa (isentropical transformation)

Δh1-2 = 52 kJ (at constant pressure)

Ideal gas equation:

P * V = m * R * T

m = (R * T) / (P * V)

R is 0.287 kJ/kg for air

m = (0.287 * 423) / (350 * 0.15) = 2.25 kg

The specifiv volume is

v0 = V0/m = 0.15 / 2.25 = 0.067 m^3/kg

Now we calculate the parameters at point 1

T1/T0 = (P1/P0)^((k-1)/k)

k for air is 1.4

T1 = T0 * (P1/P0)^((k-1)/k)

T1 = 423 * (105/350)^((1.4-1)/1.4) = 300 K

The ideal gas equation:

P0 * v0 / T0 = P1 * v1 / T1

v1 = P0 * v0 * T1 / (T0 * P1)

v1 = 350 * 0.067 * 300 / (423 * 105) = 0.16 m^3/kg

V1 = m * v1 = 2.25 * 0.16 = 0.36 m^3

The work of this transformation is:

L1 = P1*V1 - P0*V0

L1 = 105*0.36 - 350*0.15 = -14.7 kJ/kg

Q1 = 0 because it is an isentropic process.

Then the second transformation. It is at constant pressure.

P2 = P1 = 105 kPa

The enthalpy is raised in 52 kJ

Cv * T1 + P1*v1 = Cv * T2 + P2*v2 + Δh

And the idal gas equation is:

P1 * v1 / T1 = P2 * v2 / T2

T2 = T1 * P2 * v2 / (P1 * v1)

Replacing:

Cv * T1 + P1*v1 + Δh = Cv * T1 * P2 * v2 / (P1 * v1) + P2*v2

Cv * T1 + P1*v1 + Δh = v2 * (Cv * T1 * P2 / (P1 * v1) + P2)

v2 = (Cv * T1 + P1*v1 + Δh) / (Cv * T1 * P2 / (P1 * v1) + P2)

The Cv of air is 0.7 kJ/kg

v2 = (0.7 * 300 + 105*0.16 + 52) / (0.7 * 300 * 105 / (105 * 0.16) + 105) = 0.2 m^3/kg

V2 = 2.25 * 0.2 = 0.45 m^3

T2 = 300 * 105 * 0.2 / (105 * 0.16) = 375 K

The heat exchanged is Q = Δh = 52 kJ

The work is:

L2 = P2*V2 - P1*V1

L2 = 105 * 0.45 - 105 * 0.36 = 9.45 kJ

The total work is

L = L1 + L2

L = -14.7 + 9.45 = -5.25 kJ

Answer:

a) 144.000 s

b) and c)Battery voltage and power plots in attached image.

   [tex]V=-\frac{0.5}{144000} t + 1.5 V[tex]

   [tex]P(t)=-(31.25X10^{-9}) t+0.0135[/tex]  where D:{0<t<40} h

d) 1620 J

Explanation:  

a) The first answer is a rule of three

[tex]s=\frac{3600s * 40h}{1h} = 144000s[/tex]

b) Using the line equation with initial point (0 seconds, 1.5 V)

[tex]m=\frac{1-1.5}{144000-0} = \frac{-0.5}{144000}[/tex]

where m is the slope.

[tex]V-V_{1}=m(x-x_{1})[/tex]

where V is voltage in V, and t is time in seconds

[tex]V=m(t-t_{1}) + V_{1}[/tex] and using P and m.

[tex]V=-\frac{0.5}{144000} t + 1.5 V[tex]

c) Using the equation V

POWER IS DEFINED AS:

[tex] P(t) = v(t) * i(t) [tex]

so.

[tex] P(t) = 9mA * (-\frac{0.5}{144000} t + 1.5) [tex]

[tex]P(t) = - (31.25X10^{-9}) t + 0.0135[/tex]

d) Having a count that.

[tex]E = \int\limits^{144000}_{0} {P(t)} \, dt  = \int\limits^{144000}_{0} {v(t)*i(t)} \, dt[/tex]

[tex]E = \int\limits^{144000}_{0} {-\frac{0.5}{144000} t + 1.5*0.009} \, dt = 1620 J[/tex]