Question

A diatomic gas at pressure P, compressed adiabatically to half of its volume, what is the final pressure?

• A. ${\left(2\right)}^{1.4}P$
• B. $P/{\left(2\right)}^{1.4}$
• C. ${\left(2\right)}^{5/3}P$
• D. $P/{\left(2\right)}^{5/3}$

Answer 1

The correct option is A

${\left(2\right)}^{1.4}P$

For adiabatic conditions,
$P{V}^{\gamma }$ = Constant

$P_1{V_1}^{\gamma }=P_2{V_2}^{\gamma };V_2=\frac{1}{2}{V}_1$

$P_2=P_1{\left(\frac{V_1}{V_2}\right)}^{{}^{\gamma }}$
$\gamma =\frac{C_p}{C_v}=\frac{\frac{7}{2}}{\frac{5}{2}}$[For diatomic gas]
$\gamma =1.4$

$P_2=P_1{\left(\frac{V_1\times 2}{V_1}\right)}^{{}^{1.4}}$

$P_2=P_1{\left(2\right)}^{1.4}={\left(2\right)}^{1.4}P$

Hence, option (a) is the correct answer.