Five kilograms of air are used in a Carnot heat pump cycle with a coefficient of

Question

Five kilograms of air are used in a Carnot heat pump cycle with a coefficient of performance of 6.0. The system cycles 3 times per minute delivering heat to a 27 degree C room. The air receives 300 kJ of work on the 5 kg of air during the isothermal compression step, bringing it to 10 bar. Assume the air behaves ideally. What is the temperature of the other thermal reservoir? Tc = 250K = -23 degree C At which temperature does the isothermal compression occur: hot or cold? Hot What is the pressure at the beginning of the isothermal compression? 4.98 bar What is the work of the adiabatic compression step? -178.95 kJ At what rate does heat enter the heat pump? 12.5 kW

Explanation / Answer

a) here T1 = 27 C = 300 K

Now COP = 6

let other reservoir temp = T2

so, 300/(300 -T2) = 6

T2 = 250 K = -23 C

b) isothermal compression occurs at temperature of 27C i.e HOT

c) work done during isothermal compression = m.R.T ln (P2/P1) = 300 KJ (R of air = 0.287 KJ/Kg.K)

5 x 0.287 x 300 ln(10/P1) = 300

P1 = 4.98 bar

d) adiabatic work done = m x R.(T1 - T2)/y-1 for air y = 1.4

W = 5 x 0.287 x (300 -250) / (1.4-1) = 179.375 KJ

qusn (e) not clear

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