Question

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

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

Answer 1

Answer: (D)

$P \propto T^{\gamma / \gamma-1}$
$\frac{P_{2}}{P_{1}}=\left(\frac{T_{2}}{T_{1}}\right)^{\gamma / \gamma-1}$
$P_{2}=P_{1}\left(\frac{T_{2}}{T_{1}}\right)^{\gamma / \gamma-1}$
$P_{2}=2\left(\frac{1200}{300}\right)^{\frac{1.4}{1.4-1}}$
$P_{2}=256$ atm