Answer:
Option A
Explanation:
At STP ,22.4 L of any gas is 1 mole
∴ 5.6 L= \frac{5.6}{22.4}=\frac{1}{4} moles =n
In adiabatic process
T V ^{\gamma-1}= constant
\therefore T_{2} V_{2}^{\gamma-1}= T_{1} V_{1}^{\gamma-1}
or T_{2}=T_{1}\left(\frac{V_{1}}{V_{2}}\right)^{\gamma-1}
\gamma= \frac{C_{p}}{C_{V}}=\frac{5}{3} for monoatomic He gas
\therefore T_{2}= T_{1}\left(\frac{5.6}{0.7}\right)^{5/3-1}=4T_{1}
\because Further in adiabatic process
Q=0
\therefore W+ \triangle U=0
or W= -\triangle U
= -n C_{v} \triangle T
=-n\left(\frac{R}{\gamma-1}\right)(T_{2}-T_{1})
=-\frac{1}{4}\left(\frac{R}{\frac{5}{3}-1}\right)(4T_{1}-T_{1})
= -\frac{9}{8} RT_{1}
\therefore correct option is (a)
Analysis of Question
(i) From a calculation point of view question is moderately tough.
(ii) Volume of gas is decreasing. Therefore, work done by the gas should be negative.