Question

$50g$ of oxygen at $NTP$ is compressed adiabatically to a pressure of $5$ atmosphere. The work done on the gas, if $\gamma =1.4$ and $R=8.31Jmo{l}^{-1}{K}^{-1}$ is

• A. $-5173J$
• B. $1131J$
• C. $-1364J$
• D. $5673J$

Answer 1

Answer: (A)

Her, $T_1=273K,P_1=1$ atm, $P_2=5$ atm
no. of moles of oxyzen $=\frac{50}{32}$
$\Rightarrow T_2=T_1{\left(\frac{P_1}{P_2}\right)}^{\frac{\gamma -1}{\gamma }}$
$=273{\left(\frac{5}{1}\right)}^{\frac{14-1}{1.4}}$
$=273\times (5{)}^{2/7}$
$=273\times 1.584$
$=432.37$
$W=\frac{nR}{\gamma -1}[T_1-T_2]$
$=\frac{50}{32}\times \frac{8.31}{1.4-1}(273-432.37)$
$=-5173J$