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Problems:

1. On a cold day, 28100 J of heat leaks out of a house. The inside temperature is 24 °C, and the outside temperature is -10 °C. What is the increase in the entropy of the universe that this heat loss produces?

2. A concrete highway is built of slabs of 14 m long (20ºC). How wide should the expansion cracks be (at 20 ºC) between the slabs to prevent buckling if the range of temperature is -30ºC to +50 ºC?

3. In exercising, a weight lifter loses 0.171 kg of water through evaporation, the heat required to evaporate the water coming from the weight lifter's body. The work done in lifting weights is 1.95 x 10^5 J. (a) Assuming that the latent heat of vaporization of perspiration is 2.42 x 10^6 J/kg, find the change in the internal energy of the weight lifter. (b) Determine the minimum number of nutritional Calories of food that must be consumed to replace the loss of internal energy. (1 nutritional Calorie = 4186 J).

4. A gas is contained in a cylinder with a moveable piston on which a heavy block is placed. Suppose the region outside the chamber is evacuated and the total mass of the block and the movable piston is 102 kg. When 2140 J of heat flows into the gas, the internal energy of the gas increases by 1580 J. What is the distance s through which the piston rises?

5. A couple in GA win the lottery and decide to build a house in Alaska with a picture window. During the winter they keep the house heated at 25ºC while the outside temperature is -30ºC. What is the rate of heat loss via conduction through the glass window, Area=6 m^2, thickness=1.75 cm, thermal conductivity=0.80 J/(s*m*C). If instead they opted for styrofoam (thermal conductivity =0.010 J/(s*m*C)), how much less heat would they lose in one day?

6. A cylinder contains 0.250 mol of carbon dioxide gas at a temperature of 27.0 C. The cylinder is provided with a frictionless piston, which maintains a constant pressure of 1.00 atm on the gas. The gas is heated until its temperature increases to 127.0 C. Assume that the carbon dioxide can be treated as an ideal gas. 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 thermal conductivity for concrete is .8. How much heat flows through a 30 cm. thick concrete wall (area=15 m2) in 1 hour if the temp. is .0ºC on one side and 22.3ºC on the other?

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

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

10. Suppose that 2.3 mol of argon gas is heated from -45 degrees to 90ºC  Find the change in internal energy of the gas and the work it does if the heating occurs at a.) constant volume and b.) constant pressure.

11. An average adult person generally emits energy at the rate of approximately 105 W while sedentary.  At what rate is the persons entropy changing?

12. In modern steam turbine engines heat input is in the form of steam at about 600ºC  Heat is exhausted to a condenser at about 70ºC  What is the highest efficiency possible for such a steam turbine?

13. Suppose you leave a 100 W light bulb on continuously for 30 days.  If the electricity generated and delivered by the power company to the bulb at 30% efficiency, how much thermal energy does the power plant exhaust to the environment due to you oversight?

14. A mercury barometer indicates atmospheric pressure to be 761.1 torr when the temperature is 35ºC. What would the reading have been for the same atmospheric pressure if it has cooled to -10ºC?

15. What is the percent increase in volume of a glass sphere with a radius of 10 cm when it is heated from 20ºC to 100ºC?

16. A lead pellet with a mass of 0.519 g is shot from an air gun at a speed of 118 m/s. It is stopped by a boulder. What is the temperature change of the pellet? Assume the heat remains in the bullet, and the specific heat of lead is 0.0305 kcal/kg*ºC.

17. A brass ring with a coefficient of expansion 1.9X10^-5 ºC^-1 and inside diameter 17 cm at 56 ºC is heated and slipped over an aluminum rod with coefficient of expansion 2.4X10^-5 ºC^-1 and outside diameter 17.01 cm at 56 ºC. Assuming the average coefficients of linear expansion remain constant, to what temperature must this combination be cooled to separate them?

18. On a cloudy day in early January in San Antonio, a layer of ice forms in a slab that is 1.012 m wide and 1.505 m long. The ice is 7.622 mm thick. If the temperature is –1.000 °C at noon when the sun first comes out, and the ice is converted to liquid water at 5.000 °C, how long after noon was this temperature reached?

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 50.00 liter tank of helium gas is constructed from a metal that has a melting point of 1298 K. Its tensile strength is 2.026 x 10⁵ kPa (it is guaranteed not to burst until this pressure is reached). It contains 4.000 kg of helium at room temperature and it is left on a heat source that keeps getting hotter at a constant rate. If the tank is forgotten on the heat source, will it melt before it explodes, or explode before it melts?

21. A cylindrical container with a moveable piston on top is constructed with an inside diameter of 121.0mm. Inside, at the bottom of the cylinder, is a device that can generate 0.090 0g of molecular hydrogen gas. The rest of the cylinder is filled with 1.000 liter of helium gas at a pressure of 1.000atm, and all materials inside the cylinder are at a temperature of 25.00 Celsius. When the device is activated, pressure and temperature remain constant and only volume changes, what is the maximum possible distance that the piston will travel if it has a mass of 88.3g and why cant it not really travel this far?

22. Is it worth the effort to pick up a penny? Let's say a 150-lb person lowers their their center of mass 0.5 m by squatting to pick up a penny. For comparison, lets say the cost of a 300-(food)calorie donut is $1.

23. If 7.0 gm of water condenses on a 87-gm glass containing 214 gm of water at 5.0 ºC, what will be the final temperature ? Ignore the effect of the surroundings. Express your answer to the nearest tenth ºC.

24. The pendulum of a clock consists of a small heavy bob at the end of a brass rod. The clock keeps accurate time at 20ºC at which the pendulum has a period of .5520 se. By how much will it be in error after one day 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 is used to freeze 5.00 kg of water originally at 20.0 ºC to ice at -15.0 ºC. The room temperature is 25.0 ºC.
a. How much heat must be removed from the water to carry out the process described?
b. How much work is input to 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 helium gas at T = 0ºC and atmospheric pressure is 0 = 0.179 kg/m³. The temperature is then raised to T = 103ºC, but the pressure is kept constant. Assuming that helium is an ideal gas, calculate the new density of of the gas.

28. A thermopane window consists of two glass panes, each 0.50 cm thick, with a 1.0 cm thick sealed layer of air in between. If the inside surface temperature is 20.5 ºC and the outside surface temperature is 0.0 ºC, determine the rate of energy transfer through 1.5 m² of the window.

29. A volume of 2.2 m³ of air at initial conditions of 1.2 atm and 323ºC undergoes the following processes in order to complete a cycle:
(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
                          Cp = 1.005 kJ/kg K.

30. A small immersion heater is rated at 350 W. How long it will take to heat 250 mL of water from 20 ºC to 50 ºC.

31. What will be the equilibrium temperature when a 270-g block of copper at 300ºC is placed in a 150-g aluminum calorimeter cup containing 820 g of water at 12.0º?

32. A weight lifter does 1.30*10⁵ J of work lifting a weight. The weightlifter also losses 0.110 kg of water due to perspiration during this exertion. What is the weightlifter's change in internal energy? Latent heat of evaporation of water is 2.42*10⁶ J/kg.

33. A nuclear power plant operates at 79% of its maximum theoretical (Carnot) efficiency between temperatures of 660ºC and 370ºC. If the plant produces electric energy at the rate of 1.3 GW, how much exhaust 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. At 30.0 g each, how many ice cubes (originally at 0ºC) are required to cool 200 liters of water at 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. (Consider the pool and ice cubes an isolated system.)

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

38. The evaporation of perspiration is the primary mechanism for cooling the human body. Estimate the amount of water you will lose when you bake in the sun on the beach for an hour. Use the value of 1000 W/m² for the intensity of the sunlight and note that energy required to evaporate a liquid at a particular temperature is approximately equal to the sum of the energy required to raise it's temperature to the boiling point and the latent heat of vaporization (determined at the boiling point).

Answers:

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31.

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

-C_Cum_Cu(T_f - T_Cu) = C_Alm_Al(T_f - T_i) + C_wm_w(T_f - T_i)

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

T_f = 21.7 ºC

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Related Product: Equilibrium and Non-Equilibrium Statistical Thermodynamics