Question

A mass of diatomic gas $(\gamma =1.4)$ at a pressure of $2atmospheres$ is compressed adiabatically so that its temperature rises from ${27}^{o}C$ to ${927}^{o}C.$ The pressure of the gas in the final state is

• A. $256atm$
• B. $8atm$
• C. $28atm$
• D. $68.7atm$

Answer 1

Answer: (A), (D)

The correct options are
A $256atm$
D $68.7atm$

$P\infty T^{\gamma /\gamma -1}$
$\frac{P_2}{P_1}=(\frac{T_2}{T_1}{)}^{\gamma /\gamma -1}$
$P_2=P_1(\frac{T_2}{T_1}{)}^{\gamma /\gamma -1}$
$P_2=2(\frac{1200}{300}{)}^{\frac{1.4}{1.4-1}}$
$P_2=256atm$