Chapter 7, Problem 7.83P

As shown in the figure, an air conditioner operating at steady state maintains a dwelling at 70°F on a day when the outside temperature is 90°F. The rate of heat transfer into the dwelling through the walls and roof is 30,000 Btu/h and the net power input to the air conditioner compressor is 3 hp.    Determine   a. the coefficient of performance for the air conditioner b. power input required in hp c.  coefficient of performance for a reversible air conditioner providing the same cooling effect while operating between the same cold and hot temperatures.

Steady-state operating data are shown in the figure below for an open feedwater heater. Heat transfer from the feedwater heater to its surroundings occurs at an average outer surface temperature of 50°C at a rate of 100 kW. Ignore the effects of motion and gravity and let To = 25°C, po = 1 bar. Determine (a) the ratio of the incoming mass flow rates, m/ṁ2. (b) the rate of exergy destruction, in kW. P2 = 1 bar Tz = 400°C 1 ṁy = 0.7 kg/s Pi = 1 bar T, = 40°C Feedwater heater X3 = 25% P3 = 1 bar Tp = 50°C %3D 2)

At steady state, a refrigeration cycle removes 800 kJ/min of energy by heat transfer from acold space maintained at -15o C and discharges energy by heat transfer to its surroundings at20o C. If the coefficient of performance of the actual cycle is 80 percent of that of areversible refrigeration cycle (ideal) operating between thermal reservoirs at these twotemperatures (β = 0.80 βmax), determine:a) Coefficient of performance;b) Power input to the cycle, in kW;c) Heat rejected to the surroundings.Draw sketch and show all calculations.

A system undergoes a refrigeration cycle while receiving Qc by heat transfer at temperature Tc and discharging energy Qu by heat transfer at a higher temperature TH. There are no other heat transfers. (a) Using energy and exergy balances, show that the net work input to the cycle cannot be zero. (b) Show that the coefficient of performance of the cycle can be expressed as: Tc TH – TeA'¯ T(Qn – Q). B = where E, is the exergy destruction and To is the temperature of the exergy reference environment. (c) Using the result of part (b), obtain an expression for the maximum theoretical value for the coefficient of performance.

True Or False

An air conditioner is a device used to cool the inside of a home. It is, in essence, a refrigerator in which mechanical work is done and heat removed from the (cooler) inside and rejected to the (warmer) outside. A home air conditioner operating on a reversible Carnot cycle between the inside, absolute temperature T2, and the outside, absolute tempera- ture T1 > T2, consumes P joules/sec from the power lines when operating continuously. (a) In one second, the air conditioner absorbs Q2 joules from the house and rejects Q1 joules outdoors. Develop a formula for the efficiency ratio Q2/P in terms of T1 and T2. (b) Heat leakage into the house follows Newton's law Q = A(T, – T2). Develop a formula for T, in terms of T1, P, and A for continuous operation of the air conditioner under constant outside temperature T and uniform (in space) inside temperature T2. (c) The air conditioner is controlled by the usual on-off thermostat and it is observed that when the thermostat set at 20°C and an…

A reversible heat pump cycle operates at steady state between hot and cold reservoirs at TH = 30°C and Tc 10°C, respectively. The rate of heat transfer at the high temperature is 10 kW. a. Determine the net power input, in kW. b. Determine the heat transfer rate from the cold reservoir at Tc, in kW. c. Determine the coefficient of performance of the cycle.

Q1. Heat engines convert internal energy to mechanical energy. Describe the operation of this reversible engine on a PV diagram and show how to determine the efficiency of the cycle.

Example 7.1. A heat engine produces work equivalent to 80 kW with an efficiency of 40 percent. Determine the heat transfer rate to and from the working fluid.