Question

An ideal Stirling engine with air as the working fluid is considered. The temperature of the source-energy reservoir, the amount of air contained in the engine, and the maximum air pressure during the cycle are to be determined.

Assumptions: Air is an ideal gas with constant specific heats. Properties: The properties of air at room temperature are R = 0.3704 psia·ft3 /lbm.R, cp = 0.240 Btu/lbm·R, cv = 0.171 Btu/lbm·R, and k = 1.4.

Answer 1

From the thermal efficiency relation

$\eta_{th}=\frac{W_{net}}{Q_{in}}=1-\frac{T_L}{T_H}\implies \frac{2.5}{6}=1-\frac{510}{T_H}\implies T_H=874$ R

State 3 may be used to determine the mass of air in the system:

$m=\frac{P_3V_3}{RT_3}=\frac{10\cdot0.5}{0.3704\cdot510}=0.02647$ lbm

The maximum pressure occurs at state 1:

$P_1=\frac{mRT_1}{V_1}=\frac{0.02647\cdot0.3704\cdot874}{0.06}=143$ psia