Question

A Gas power cycle operating between the pressure limits of 1 bar and 7 bar, has minimum and maximum temperature of 300 K and 1600 K. Ratio of sspecific heat of working fluid is 1.4. If the compression is polytropic with index 1.3 and expansion process is isentropic and other processes are isobaric. Approximate final temperature in ${}^{\circ }C$ at the end of compression and expansion respectively are

• A. 197, 645
• B. 197, 917
• C. 470,917
• D. 470,645

Answer 1

The correct option is A 197, 645

$\frac{T_2}{T_1}={\left(\frac{P_2}{P_1}\right)}^{\frac{n-1}{n}}$
$T_2=T_1\times {\left(\frac{P_2}{P_1}\right)}^{\frac{n-1}{n}}=300\times {\left(\frac{7}{1}\right)}^{\frac{1.3-1}{1.3}}$
$T_2=470K={197}^{\circ }C$
$\frac{T_s}{T_4}={\left(\frac{P_3}{P_4}\right)}^{\frac{\gamma -1}{\gamma }}$
$T_4=\frac{T_5}{(P_3/P_4{)}^{\frac{\gamma -1}{\gamma }}}=\frac{1600}{(7{)}^{1.4-1/1.4}}$
$T_4=917.62K={644.62}^{\circ }C$