SMES1202 Thermal Physics Semester 2 2007/2008 Tutorial 5

[Note: The problems below are from Sears and Salinger]

  1. Find the change in entropy of the system during the following processes: (a) 1 kg of ice at 0°C and 1 atm pressure melts at the same temperature and pressure. The latent heat of fusion is . (b) 1 kg of steam at 100°C and one atm pressure condenses to water at the same temperature and pressure. The latent heat of vaporization is. [S&S:5-3]
  2. A system is taken reversibly around the cycle a-b-c-d-a shown in Fig. 1. The temperatures t are given in degrees Celsius. Assume that the heat capacities are independent of temperature and and. (a) Calculate the heat flow Q into the system in each portion of the cycle. According to the first law, what is the significance of the sum of these heat flows? (b) If and, calculate the pressure difference . (c) Calculate the value of along each portion of the cycle. According to the second law, what is the significance of the value of the sums of these integrals? (d) Suppose that a temperature were defined as the Celsius temperature plus some value other than 273.15. Would it then be true that ? Explain. [S&S:5-4] Fig. 1
  3. A 50-ohm resistor carrying a constant current of 1 A is kept at a constant temperature of 27°C by a stream of cooling water. In a time interval of 1 s, (a) what is the change in entropy of the resistor? (b) what is the change in entropy of the universe? [S&S:5-5]
  4. A thermally insulated 50-ohm resistor carries a current of 1 A for 1 s. The initial temperature of the resistor is 10°C, its mass is 5 g, and its specific heat capacity is . (a) What is the change in entropy of the resistor? (b) What is the change in entropy of the universe? [S&S:5-9]
  5. A system is taken reversibly around the cycle a-b-c-d-a shown on the T-S diagram of Fig. 2. (a) Does the cycle a-b-c-d-a operate as an engine or a refrigerator? (b) Calculate the heat transferred in each process. (c) Find the efficiency of this cycle operating as an engine graphically as well as by direct calculation. (d) What is the coefficient of performance of this cycle operating as a refrigerator? [S&S:5-13]

Fig. 2

  1. Show that if a body at temperature T1 is brought in contact with a heat reservoir at temperature T2T1, the entropy of the universe increases. Assume that the heat capacity of the body is constant. [S&S:5-14]
  2. An inventor claims to have developed an engine that takes in 107 J at a temperature of 400 K, rejects at a temperature of 200 K, and delivers of mechanical work. Would you advise investing money to put this engine on the market? How would you describe this engine? [S&S:5-27]