Question

At ${27}^{o}C$ a gas compressed suddenly such that its pressure becomes 32 times the original pressure. The amount of useful work done is: $(\gamma =5/3)$

• A. $11.2\times {10}^{3}Joule$
• B. $3.8\times {10}^{4}Joule$
• C. $5.9\times {10}^{5}Joule$
• D. $9.3\times {10}^{6}Joule$

Answer 1

Answer: (A)

$11.2\times {10}^{3}Joule$

Sudden compression of the gas implies that the process is almost adiabatic process.
Work done in an adiabatic process is
$W=n{C}_v\Delta T=\frac{nR\Delta T}{\gamma -1}$
In an adiabatic process
${\left(\frac{P_1}{P_2}\right)}^{1-\gamma }={\left(\frac{T_2}{T_1}\right)}^{\gamma }$
$(\frac{1}{32}{)}^{1-\frac{5}{3}}={\left(\frac{T_2}{300}\right)}^{\frac{5}{3}}$
${32}^{\left(2/5\right)}=\frac{T_2}{300}$
$\frac{T_2}{300}=4$
$T_2=1200K$
$W=\frac{\left(8.314\right)(1200-300)}{\frac{5}{3}-1}=11223.9J=11.2\times {10}^{3}J$
Option A.