Due: September 29, 2006 (12:00 Noon @ ECAE 131, TA’s office)
1. (15 points) One kilogram of water at 0ºC is heated to 100ºC. Compute its change in entropy.
Answer: (10 points for the correct equations, 5 points for the correct answer) The temperature is not constant and dQ and T must be expressed in termes of a single variable in order to carry out the integration.
2. (15 points) A new design of a household water heater is 60 cm in diameter and 153 cm tall. The outside surface is designed to remain constant at 26 ºC for an ambient air temperature of 20 ºC and a convective heat transfer coefficient of 10 W/(m2 * ºC). Assume no heat transfer on the floor of the water heater
Determine (a) the rate of heat loss from the water heater in W; and (b) determine the rate of entropy transfer accompanying heat transfer in W/K. Show your equations and list your assumptions for credit.
3. (20 points) Suppose 1 kg of water at 100ºC is placed in thermal contact with 1 kg of water at 0ºC. What is the total change in entropy?
Answer: (10 points for the correct equations, 10 points for the correct answers) Assume the specific heat of water is constant in this temperature range. Then the entropy change of the hot water is:
4. (25 points) During the isothermal heat rejection process of a Carnot cycle, the working fluid experiences an entropy change of -1.8 kJ/K. If the temperature of the energy sink is 15 ºC, determine (a) the amount of heat transfer to the sink, (b) the entropy change of the sink, and (c) the total entropy generation for this process. Show your equations and list your assumptions for credit.
Answer: (5 points for assumptions, 15 points for equations, 5 points for correct answer)
Assumptions, Isothermal heat transfer process, no entropy generated during this process.
However, the entropy balance for the fluid can be calculated as:
(a) 7 points
The entropy change of the sink is determined from the heat transfer from the fluid to the sink
(b) 7 points
(c) 6 points
5. (25 points) An insulated piston-cylinder device initially contains 500L of air at 101 kPa and 37 ºC. Air is now heated for 20 min by a 300W resistance heater placed inside the cylinder. The pressure of air is maintained constant during this process. Determine (a) the entropy change of the air in kJ/K. Show your equations and list your assumptions for credit. For this problem, use a constant Cp at 600K.
Answer: (5 points for assumptions, 15 points for equations, 5 points for correct answers)
Assume air is an ideal gas.
The first law relation for the constant pressure process of this adiabatic system simplifies to:
Using a constant Cp value at 600K, 1.051 kJ/(kg*K)