Kinetic Theory - Result Question 7
7. A gas at $27^{\circ} C$ temperature and 30 atmospheric pressure is allowed to expand to the atmospheric pressure. If the volume becomes 10 times its initial volume, then the final temperature becomes
(a) $100^{\circ} C$
(b) $173^{\circ} C$
(c) $273^{\circ} C$
(d) $-173^{\circ} C$
[2001]
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Answer:
Correct Answer: 7. (d)
Solution:
- (d) Given : Initial temperature of gas
$(T_1)=27^{\circ} C=300 K$
Initial pressure $(P_1)=30 atm$
Initial volume $(V_1)=V$
Final pressure $(P_2)=1 atm$
Final volume $(V_2)=10 V$.
We know from the general gas equation that $\frac{P_1 V_1}{T_1}=\frac{P_2 V_2}{T_2} \quad$ or, $\quad \frac{30 \times V}{300}=\frac{1 \times 10 V}{T_2}$
or, $T_2=100 K=-173^{\circ} C$.
