JEE PYQ: Thermodynamics Question 34
Question 34 - 2019 (10 Jan Shift 2)
An ideal gas undergoes isothermal compression from 5 m$^3$ to 1 m$^3$ against a constant external pressure of 4 Nm$^{-2}$. Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 J mol$^{-1}$ K$^{-1}$, the temperature of Al increases by:
(1) $\dfrac{3}{2}$ K
(2) 2 K
(3) $\dfrac{2}{3}$ K
(4) 1 K
Show Answer
Answer: (3)
Solution
We know that, $w = -P_{ext}(V_f - V_i) = -4 \times (1 - 5) = 16$ J. For isothermal compression, $\Delta U = q + w$. $q = -w = -16$ J ($\Delta U = 0$ for isothermal process). From calorimetry, Heat given $= nC\Delta T$. $16 = \dfrac{1 \times 24 \times \Delta T}{\text{mol K}}$. $\Delta T = \dfrac{2}{3}$ K.
BETA
