Question

The rise in temperature of an ideal gas ($Y=5/3$) when at ${27}^{o}C$ it is adiabatically compressed to $\frac{8}{27}$ of its original volume is:

• A. ${450}^{o}C$
• B. ${375}^{o}C$
• C. ${225}^{o}C$
• D. ${402}^{o}C$

Answer 1

Answer: (D)

${402}^{o}C$

${TV}^{\gamma -1}=$constant
$T_1[\frac{8V}{27}{]}^{\gamma -1}=$constant
$\therefore \frac{T_1}{T}\times [\frac{8}{27}{]}^{5/3-1}=1$
or $T_1=[\frac{27}{8}{]}^{2/3}\times T$
$=2.25\times 300$
$=675K={402}^{o}C$