Heat and Thermodynamics 6 Question 12
16. Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be
(2014 Adv.)
(a) $550 K$
(b) $525 K$
(c) $513 K$
(d) $490 K$
Show Answer
Answer:
Correct Answer: 16. (a)
Solution:
- Let final equilibrium temperature of gases is $T$ Heat rejected by gas by lower compartment
$$ =n C _V \Delta T=2 \times \frac{3}{2} R(700-T) $$
Heat received by the gas in above compartment
$$ =n C _p \Delta T=2 \times \frac{7}{2} R(T-400) $$
Equating the two, we get
$$ \begin{aligned} 2100-3 T & =7 T-2800 \\ \Rightarrow \quad T & =490 K \end{aligned} $$
