Additional Problems

| 74 | One-half mole of a monatomic ideal gas expands adiabatically and does 610 J of work. By how many kelvins does its temperature change? Specify whether the change is an increase or a decrease.

| 75 | ssm Three moles of an ideal gas are compressed from to . During the compression, of work is done on the gas, and heat is removed to keep the temperature of the gas constant at all times. Find (a) , (b) Q, and (c) the temperature of the gas.

| 76 | Multiple-Concept Example 6 deals with the same concepts as this problem does. What is the efficiency of a heat engine that uses an input heat of and rejects of heat?

| 77 | A gas is contained in a chamber such as that in Figure 15-5. Suppose the region outside the chamber is evacuated and the total mass of the block and the movable piston is 135 kg. When 2050 J of heat flows into the gas, the internal energy of the gas increases by 1730 J. What is the distance S through which the piston rises?

| 78 | The inside of a Carnot refrigerator is maintained at a temperature of 277 K, while the temperature in the kitchen is 299 K. Using 2500 J of work, how much heat can this refrigerator remove from its inside compartment?

| 79 | ssm Find the change in entropy of the H2O molecules when (a) three kilograms of ice melts into water at 273 K and (b) three kilograms of water changes into steam at 373 K. (c) On the basis of the answers to parts (a) and (b), discuss which change creates more disorder in the collection of H2O molecules.

| 80 | The temperature of 2.5 mol of helium (a monatomic gas) is lowered by 35 K under conditions of constant volume. Assuming that helium behaves as an ideal gas, how much heat is removed from the gas?

| 81 | A Carnot heat pump operates between an outdoor temperature of 265 K and an indoor temperature of 298 K. Find its coefficient of performance.

| 82 | An engine does 18 500 J of work and rejects 6550 J of heat into a cold reservoir whose temperature is 285 K. What would be the smallest possible temperature of the hot reservoir?

| 83 | ssm The volume of a gas is changed along the curved line between A and B in the drawing. Do not assume that the curved line is an isotherm or that the gas is ideal. (a) Find the magnitude of the work for the process, and (b) determine whether the work is positive or negative.

* | 84 | Refer to the drawing in problem 83, where the curve between A and B is now an isotherm. An ideal gas begins at A and is changed along the horizontal line from A to C and then along the vertical line from C to B. (a) Find the heat for the process ACB and (b) determine whether it flows into or out of the gas.

| 85 | ssm A monatomic ideal gas expands at constant pressure, (a) What percentage of the heat being supplied to the gas is used to increase the internal energy of the gas? (b) What percentage is used for doing the work of expansion?

* | 86 | Interactive LearningWare 15.2 at explores one approach to problems such as this. Two kilograms of liquid water at 0 °C is put into the freezer compartment of a Carnot refrigerator. The temperature of the compartment is −15 °C, and the temperature of the kitchen is 27 °C. If the cost of electrical energy is ten cents per kilowatt · hour, how much does it cost to make two kilograms of ice at 0 °C?

* | 87 | Refer to Interactive Solution 15.87 at for help in solving this problem. A diesel engine does not use spark plugs to ignite the fuel and air in the cylinders. Instead, the temperature required to ignite the fuel occurs because the pistons compress the air in the cylinders. Suppose air at an initial temperature of 21 °C is compressed adiabatically to a temperature of 688 °C. Assume the air to be an ideal gas for which . Find the compression ratio, which is the ratio of the initial volume to the final volume.

* | 88 | Suppose that 31.4 J of heat is added to an ideal gas. The gas expands at a constant pressure of while changing its volume from to . The gas is not monatomic, so the relation does not apply. (a) Determine the change in the internal energy of the gas. (b) Calculate its molar specific heat capacity CP.

* | 89 | A monatomic ideal gas is heated while at a constant volume of , using a ten-watt heater. The pressure of the gas in creases by . How long was the heater on?

* | 90 | From a hot reservoir at a temperature of T1, Carnot engine A takes an input heat of 5550 J, delivers 1750 J of work, and rejects heat to a cold reservoir that has a temperature of 503 K. This cold reservoir at 503 K also serves as the hot reservoir for Carnot engine B, which uses the rejected heat of the first engine as input heat. Engine B also delivers 1750 J of work, while rejecting heat to an even colder reservoir that has a temperature of T2. Find the temperatures (a) T1 and (b) T2.

** | 91 | ssm An engine has an efficiency e1. The engine takes input heat of magnitude |QH| from a hot reservoir and delivers work of magnitude |W1|. The heat rejected by this engine is used as input heat for a second engine, which has an efficiency e2 and delivers work of magnitude |W2|. The overall efficiency of this two-engine device is the magnitude of the total work delivered () divided by the magnitude |QH| of the input heat. Find an expression for the overall efficiency e in terms of e1 and e2.

** | 92 | The drawing shows an adiabatically isolated cylinder that is divided initially into two identical parts by an adiabatic partition. Both sides contain one mole of a monatomic ideal gas ( ), with the initial temperature being 525 K on the left and 275 K on the right. The partition is then allowed to move slowly (i.e., quasi-statically) to the right, until the pressures on each side of the partition are the same. Find the final temperatures on the (a) left and (b) right.

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