JEE PYQ: Thermodynamics Question 20
Question 20 - 2020 (04 Sep Shift 1)
A closed vessel contains 0.1 mole of a monatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to __________.
Show Answer
Answer: 266.67
Solution
Here work done on gas and heat supplied to the gas are zero. Let $T$ be the final equilibrium temperature of the gas in the vessel.
Total internal energy of gases remain same.
i.e., $u_1 + u_2 = u_1’ + u_2'$
$n_1 C_v \Delta T_1 + n_2 C_v \Delta T_2 = (n_1 + n_2) C_v T$
$(0.1)C_v(200) + (0.05)C_v(400) = (0.15)C_v T$
$\therefore T = \frac{800}{3} = 266.67$ K
BETA
