Question

A Carnot power cycle operates on 2lb/min of air between the limits of 70F and 500

F. The pressure at the beginning of isothermal expansions is 400 psia and at the end

of isothermal expansion 185.psig, determine;

a. The volume at the end of the isothermal compression

b. ∆S during an isothermal process

c. Qa, Qr, Wnet

d. Thermal efficiency

e. The mean effective pressure.

Answer 1

Solution;

m=2lb

(a)

$P_1=400psia$

$P_2=199.7psia$

$V_1=\frac{mRT_1}{P_1}=\frac{2×53.34×960}{400×144}=1.778ft^3$

$V_2=\frac{mRT_2}{P_2}$

$V_2=\frac{2(53.34)(960)}{199.7×144}=3.561ft^3$

$V_3=\frac{mRT_3}{p_3}$

$V_3=\frac{2(53.34)×530}{24.97×144}=7.849ft^3$

(b)

$\Delta S_{1-2}=mRln\frac{v_2}{v_1}$

$\Delta S_{1-2}=2×\frac{53.34}{778}ln\frac{3.561}{1.778}=0.0952Btu/°R$

(c)

$Q_a=T_1\Delta s=960×0.0952=91.43Btu$

$Q_r=-T_3\Delta s=-530×0.0952=-50.46Btu$

(d)

$\eta=\frac{W}{Q}$

$W=Q_a-Q_r$ =40.97Btu

$\eta=\frac{40.97}{91.43}=0.4481$