During the isothermal expansion stroke of the idealized Stir

During the isothermal expansion stroke of the idealized Stirling cycle shown, the right hand piston remains fixed as the left hand piston travels downward. Find the heat added (Q_H) given the following: Working fluid is air Piston diameter; d_piston = 75cm Combined piston height at time of movement; h_c + h_h = 1 m Atmospheric pressure; P_atm = 100 kPa Chamber pressure at time of movement; P_initial = 500kPa Force opposing piston motion; F_piston = 44 kN

Solution

Piston area A = 3.14/4*0.75^2 = 0.4416 m^2

Resisting pressure = F/A = 44 / 0.4416 = 99.646 kPa

Pressure at end of expansion stroke P2 = 100 + 99.646 = 199.646 kPa ~ 200 kPa

Initial volume V1 = 3.14/4*0.75^2*1 = 0.4416 m^3

Q = P1*V1 ln (P1/P2)

= 500*0.4416*ln(500/200)

= 202.3 kJ