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