A volume of air (assumed to be an ideal gas) is first cooled without changing its volume and then expanded without changing its pressure, as shown by path ?abc in Fig. P19.39?. (a) How does the final temperature of the gas compare with its initial temperature? (b) How much heat does the air exchange with its surroundings during process ?abc?? Does the air absorb heat or release heat during this process? Explain. (c) If the air instead expands from state a to state c by the straight-line path shown, how much heat does it exchange with its surroundings?

Solution 43P This question is based on the first law of thermodynamics, which is expressed mathematically as Q = U + W , where Q is the amount of heat added to a system, U is the change in internal energy of the system and W is the work done by the system. (a) et the initial temperature of the gas at point a be T. From point a to b, the volume of the gas remains constant. According to Gay-Lussac’s law, when the volume of a gas is constant, its pressure is directly proportional to temperature. From a to b, the pressure of the gas becomes rd of the initial value. Therefore, the temperature will also be rd of the initial temperature. Therefore, at the point b, the temperature will be /3. Now, from state b to c, the pressure of the gas remains constant, but volume increases by three times. According to Charles’ law, when pressure remains constant for a gas, volume and temperature are directly proportional to each other. Therefore, temperature from the state b to c will also increase by three times. Therefore, the temperature of the gas at state c is = T/3 × 3 =...