JEE Advance - Physics (2022 - Paper 1 Online - No. 17)
List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.
| List-I | List-II |
|---|---|
| (I) $10^{-3} \mathrm{~kg}$ of water at $100^{\circ} \mathrm{C}$ is converted to steam at the same temperature, at a pressure of $10^{5} \mathrm{~Pa}$. The volume of the system changes from $10^{-6} \mathrm{~m}^{3}$ to $10^{-3} \mathrm{~m}^{3}$ in the process. Latent heat of water $=2250\, \mathrm{~kJ} / \mathrm{kg}$. |
(P) $2 \mathrm{~kJ}$ |
| (II) $0.2$ moles of a rigid diatomic ideal gas with volume $V$ at temperature $500 \mathrm{~K}$ undergoes an isobaric expansion to volume $3 \mathrm{~V}$. Assume $R=8.0 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$. |
(Q) $7 k J$ |
| (III) One mole of a monatomic ideal gas is compressed adiabatically from volume $V=\frac{1}{3} \mathrm{~m}^{3}$ and pressure $2 \mathrm{kPa}$ to volume $\frac{V}{8}$. |
(R) $4 \mathrm{~kJ}$ |
| (IV) Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 \mathrm{~kJ}$ of heat and undergoes isobaric expansion. |
(S) $5 \mathrm{~kJ}$ |
| (T) $3 \mathrm{~kJ}$ |
Which one of the following options is correct?
Explanation
$$U = ML - P\Delta V$$
$$ = {10^{ - 3}} \times 2250 - {10^2}kP \times ({10^{ - 3}} - {10^{ - 6}})$$ m3
= 2.25 kJ $$-$$ 0.1 kJ
= 2.15 kJ
I $$\to$$ P
(II) $${C_V} = {{5R} \over 2}$$ (rigid diatomic)
For isobaric expansion
$$V \propto T$$
$${{{V_1}} \over {{V_2}}} = {{{T_1}} \over {{T_2}}} \Rightarrow {V \over {3V}} = {{500} \over {{T_2}}} \Rightarrow {T_2} = 1500\,K$$
$$\Delta U = n{C_V}\Delta T = 0.2 \times {{5 \times 8} \over 2} \times (1500 - 500)$$ J = 4 kJ
II $$\to$$ R
(III) Adiabatic expansion $$\left( {\gamma = {5 \over 3}} \right)$$
$${P_1}V_1^\gamma = {P_2}V_2^\gamma \Rightarrow $$ (2 kPa) $$ \times V_0^{5/3} = {P_2} \times {\left( {{{{V_0}} \over 8}} \right)^{5/3}}$$
$${P_2} = 64$$ kPa
$$\Delta U = n{C_V}\Delta T$$
$$ = {{3nR\Delta T} \over 2} = {3 \over 2}({P_2}{V_2} - {P_1}{V_1}) = {3 \over 2} \times \left( {64 \times {1 \over {3 \times 8}} - 2 \times {1 \over 3}} \right)$$
$$ = {3 \over 2} \times \left( {{8 \over 3} - {2 \over 3}} \right) = 3$$ kJ
III $$\to$$ T
(IV) For isobaric expaision,
$$\Delta U = n{C_V}\Delta T = {7 \over 2}\,nR\Delta T$$
$$\Delta Q = n{C_P}\Delta T = {9 \over 2}\,nR\Delta T$$
$${{\Delta U} \over {\Delta Q}} = {7 \over 9}$$
$$\Delta U = {7 \over 9}\Delta Q = 7$$ kJ
IV $$\to$$ Q
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