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Thermodynamics

Thermodynamics Problems

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1. When the temperature inside a particular house is 24 °C and the temperature outside is -10 °C, 28100 J of heat leaks out of the house. What increase in the entropy of the universe does this heat loss produce?

2. Concrete slabs 14 m long (20ºC) are subjected to temperature variations from -30ºC to +50 ºC. How wide should the expansion cracks be (at 20 ºC)?

3. A car is consuming 10 kg of gasoline per hour with an efficiency of 25%.  If gasoline releases 46,000 J/gram of heat, what is the average horsepower output of the engine? (1 hp = 746 W).

4. A vertical cylinder containing a gas is closed at the bottom and sealed by a movable frictionless piston at the top end. A block is placed on the piston. The combined mass of the block and piston is 102 kg. When 2140 J is added to the system, the internal energy of the gas increases by 1580 J. What distance does the block rise?

5. A house is heated to a constant 25 oC while the outside temperature is -30 oC. What is the rate of heat loss through a closed sealed single-pane window having an area=6 m2, thickness=1.75 cm, and thermal conductivity=0.80 J/(s*m*C). If the glass was replaced with styrofoam (thermal conductivity =0.010 J/(s*m*C)), how much less heat would be lost in one day?

6. A cylinder contains 0.250 mol of ideal gas at 27.0 C. A constant pressure of 1.00 atm is maintained by a frictionless piston. If the gas is heated to 127.0 C:
a. How much work is done by the gas in this process?
b. On what is this work done?
c. What is the change in internal energy of the gas?
d. How much heat was supplied to the gas?

7. The air outside a 30 cm. thick wall (area=15 m2) is 0 degrees Celsius and 22.3 degrees celsius on the other side. If the thermal conductivity of the wall is .8 how much heat is conducted by the wall in 1 hour?

8. What is the R value for a 1.4 cm thick layer of a.) glass (Kg. =.80) b.) plywood? (Kp=.085 W/K *m)

9. By how much has the internal energy of a 2.2 Kg. block of ice change when it melts to water at 0 degree celsius?  Neglect the small change in volume.

10. Find the change in internal energy of 2.3 mol of argon gas (number of freedom, i = 3) and the work it does when it is heated from -45 degrees to 90 degrees celsius at
a. constant volume
b. constant pressure.

11. A body at 37 degrees Celsius is emitting energy at the rate of approximately 105 W.  At what rate is the entropy changing?

12. Steam is injected into an engine at 600 degrees Celsius and exhausts at 70 degrees Celsius  What is the highest efficiency possible of this engine?

13. A 100 W light bulb is left on for 30 days.  If electricity is generated with 30% efficiency, how much energy is released to the environment?

14. An engine with a Carnot efficiency of 20 percent operates between a high temperature T1 and a low temperature T2 = 47 0C.  What is the high temperature?

15. A glass sphere (10 cm radius) is heated from 20ºC to 100ºC. What is its percent increase in volume?

16. A 0.519 g lead pellet traveling at 118 m/s is stopped by a boulder. Neglecting any heat lost by the pellet, what is the temperature change of the pellet? The specific heat of lead is 0.0305 kcal/kg*ºC.

17. A brass ring with an inside diameter 17 cm at 56 ºC is heated, slipped over an aluminum rod with an outside diameter 17.01 cm at 56 ºC and allowed to cool. At what temperature may this combination be separated? (coefficients of linear expansion: brass = 1.9X10-5 ºC-1 ; aluminum = 2.4X10-5 ºC-1)

18. A layer of ice is 1.012 m wide, 1.505 m long and 7.622 mm thick. The ice, originally at –1.000 °C, receives solar radiation at 300 W / m2, and is converted to liquid water at 5.000 °C How much time does this process take?

19. At standard pressure, what would the temperature of water molecules be if they had a root mean square (rms) velocity of 5.87 m/s?

20. A particular alloy has a melting point of 1298 K and a tensile strength of 2.026 x 105 kPa. It is used to construct a 50.00L tank that contains 4.000 kg of helium at room temperature. If it is slowly heated, will it melt first or explode?

21. A vertical cylinder with an inside diameter of 121.0mm and a 88.3g piston on top contains 1.000 liter of helium gas. While 0.0900g of hydrogen gas are injected into the cylinder, the cylinder and its contents maintain a temperature of 25.00 Celsius and a pressure of 1.000atm. What is the maximum distance the piston will travel? Why will it not travel this far?

22. If a 150-lb person lowers their center of mass 0.5 m by squatting to pick up a penny, and the cost of a 300-(food)calorie donut is $1, is it worth the effort to pick up a penny?

23. An 87g glass containing 214g of water, and the surrounding air, are at 5.0 ºC. What will be the final temperature of the glass-water system after 7.0g of water condenses onto the glass, and if there is negligible heat exchange between the system and the surroundings?

24. The timing of a clock is controlled by a brass pendulum. The pendulum has a period of 0.5520s at 20ºC. How long will the clock take to loose one minute at 35ºC?

25. After 2.0 kg of mercury gained 2.52 X 104 J of heat energy, its final temperature was 130 ºC. What was its initial temperature?

26. A Carnot refrigerator cools 5.00 kg of water at 20.0ºC to ice at -15.0ºC. The room temperature is 25.0ºC.
a. How much heat must be removed from the water?
b. How much work is put into the refrigerator?
c. What is the coefficient of performance of the refrigerator?
heat capacities: water 4.186 kJ/kg*K ice 2.05 kJ/kg*K
latent heat water 333.5 kJ/kg

27. The density of an ideal gas at 0ºC and atmospheric pressure is 0 = 0.179 kg/m3. What density would the gas have if temperature is then raised to 103ºC, at constant pressure?

28. A sealed window is made of two 0.50 cm thick glass panes and a 1.0 cm thick layer of air in between. Determine the rate of energy transfer through 1.5 m2 of the window when the surface temperature inside is 20.5 ºC outside is 0.0 ºC.

29. A volume of 2.2 m3 of air at 1.2 atm and 323ºC ("state 1") is subjected to the following sequence:
(i) isothermal compression from state 1 through a volumetric compression ratio of 45 (rv) to state 2
(ii) isobaric expansion from state 2 back to the initial volume thus reaching state 3
(iii) isochoric cooling from state 3 back to the original pressure to return to state 1.

For this sequence of processes, sketch a fully annotated p-V diagram & determine:
(i) the mass of air present
(ii) the maximum pressure in the cycle
(iii) the maximum temperature in the cycle
(iv) the total heat transfer in the isobaric expansion
(v) the net work done in the cycle.

Assume for air: R = 0.287 kJ/kg K and Cp = 1.005 kJ/kg K.

30. How long it will take a 350 W immersion heater to heat 250 mL of water from 20 ºC to 50 ºC?

31. What will be the final temperature of a system consisting of a 150-g aluminum cup containing 820 g of water at 12.0º and a 270-g block of copper at 300ºC?

32. A laborer does 1.30*105 J of work and losses 0.110 kg of water due to perspiration. What is the laborer's change in internal energy? Latent heat of evaporation of water is 2.42*106 J/kg.

33. A plant generates 1.3 GW of electricity while operating at 79% of its maximum theoretical (Carnot) efficiency between temperatures of 660ºC and 370ºC. How much waste heat is discharged per hour?

34. 1.0 kg of water at 40ºC is mixed with 1.0 kg of ice at -20ºC in a thermally isolated container. How much ice remains when thermal equilibrium is reached?

35. For an isolated system, how many 30.0 g ice cubes (originally at 0ºC) are required to cool 200 liters of water from 25ºC to 16ºC? The density of water is 1000 kg/m3, the specific heat of water is 1.0 cal/gºC, the specific heat of ice is 0.5 cal/gºC, and the latent heat of fusion of water is 80 cal/g.

36. How much energy is required to raise the temperature of 5 kilograms of coal from 20ºC to 220ºC?

37. A hole in a steel plate has a 0.99970cm diameter at 300ºC. To what temperature must the plate be heated for the hole to have a diameter of 1.00000 cm?

38. What mass of storage rock cools from 65 oC to 22 oC while losing 5 x107 cal of heat? (Specific heat of rocks is 0.21 cal/g-oC)

Answers to Thermodynamics Problems

For solutions to all the problems on this page click here.

31.

symbol quantity value
TCu initial temperature of copper 300ºC
Ti initial temperature of aluminum and water 12.0ºC
mCu mass of copper 270 g
mAl mass of aluminum 150 g
mw mass of water 820 g
CCu specific heat of copper 0.38 J/gK
CAl specific heat of aluminum 0.92 J/gK
Cw specific heat of water 4.186 J/gK
Tf equilibrium temperature ? ºC

The heat lost by the copper is the heat gained by the aluminum and water if the heat loss to the surroundings is negligible.

-CCumCu(Tf - TCu) = CAlmAl(Tf - Ti) + Cwmw(Tf - Ti)

-(0.38)(270)(Tf - 300 ) = (0.92)(150)(Tf - 12 ) + (4.186)(820)(Tf - 12 )

Tf = 21.7 ºC

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