Question

An air compressor takes shaft work of 200 kJ/kg and compression increases enthalpy by 100 kJ/kg of air. Cooling water picks up 90 kJ/kg of air of heat while cooling. Determine the heat transferred (Qa + Qw) from the compressor to the atmosphere.​

Answer 1

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S} \blue{W} \purple{E} \orange{R: }}}}$

$\text{Work interaction, W = – 200 kJ/kg of air}\\\text{Increase in enthalpy of air = 100 kJ/kg of air}\\\text{Total heat interaction,} \\ \text{Q = Heat transferred to water + Heat transferred to atmosphere.}\\\text{Writing steady flow energy equation} \\\text{on compressor, for unit mass of air entering at 1 and leaving at 2.}\\                                                     h_{1} + \frac{C_{1}^{2}}{2} + gZ_{1} + Q = h_{2} + \frac{C_{2}^{2}}{2} + gZ_{2} + W\\\text{Assuming no change in potential energy and kinetic energy;}\\\begin{aligned}\Delta KE&= \Delta PE = 0\\Q&= (h_{2}  –  h_{1}) + W\\&= 100 + (- 200)\\Q&= -100 \text{ kJ/kg of air}\\\text{Also}                                                                                                        &\\Q&= – 100 = \text{Heat transferred to water + Heat transferred to atmosphere}\\\text{or}                                                                                                               &\\- 100&= (-90) + \text{Heat transferred to atmosphere}\\\text{Heat transferred to atmosphere}&= \textbf{- 10 kJ/kg }\text{of air}\end{aligned}$