Question

Helium gas is throttled steadily from 300 kPa and 50°C. Heat is lost from the Helium in the amount of 1.75 kJ/kg to the surroundings at 25°C and 100 kPa. If the entropy of the helium increases by 0.25 kJ/kg.K, determine its exit temperature and pressure.
(Assume, $C_p$ = 5.19 kJ/kg.K, R = 2.07 kJ/kg.K for Helium)

• A. 0°C, 265 kPa
• B. 0°C, 150 kPa
• C. 49.7°C, 265 kPa
• D. 49.7°C, 150 kPa

Answer 1

The correct option is C 49.7°C, 265 kPa

Using steady flow energy equation for unit mass

$h_1+\frac{V_1^2}{2}+\frac{dQ}{dm}=h_2+\frac{V_2^2}{2}+\frac{dW}{dm}$

$h_1+\frac{dQ}{dm}=h_2[\because \frac{dW}{dm}=0,V_{1}and{V}_{2}arenegligible]$

$C_p{T}_1+\frac{dQ}{dm}=C_p{T}_2$

$\Rightarrow 5.19\times 50-1.75=5.19\times T_2$

$\Rightarrow T_2=49.7{}^{\circ }C$

$S_2-S_1=C_p\ell n\left(\frac{T_2}{T_1}\right)-R\ell n\left(\frac{P_2}{P_1}\right)$

$0.25=5.19\ell n\left(\frac{49.7+273}{50+273}\right)-2.07\ell n\left(\frac{P_2}{300}\right)$

$\Rightarrow P_2=265kPa$