Question

An ideal compressor compresses 12kg/min of air isothermally from 99kPa and a specific volume of 0.81m^2/kg to a final pressure of 600kPa. Determine a)power(kw) required to drive the compressor b. change in entropy(kJ/K) c. heat transferred

Answer 1

$W =-\int{VdP} = -P_1V_1\ln\dfrac{P_2}{P_1} = mRT_1\ln\dfrac{P_1}{P_2}$

$P_1V_1 = RT_1\\$

$T_1 = \dfrac{99 × 0.81}{0.287} = 279.4K$

$W =- 12( 0.287)(279.4)ln\dfrac{99}{600}= -17338kJ/min$

$= -29kW$

Work is done on the system, because Work done is negative. There is a decrease in volume.

Heat transferred into the system is 17338J in one minute.