1
JEE Advanced 2023 Paper 2 Online
+3
-1
An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is $n$. The internal energy of one mole of the gas is $U_n$ and the speed of sound in the gas is $\mathrm{v}_n$. At a fixed temperature and pressure, which of the following is the correct option?
A
$v_3 < v_6$ and $U_3 > U_6$
B
$v_5 > v_3$ and $U_3 > U_5$
C
$v_5 > v_7$ and $U_5 < U_7$
D
$v_6 < v_7$ and $U_6 < U_7$
2
JEE Advanced 2023 Paper 1 Online
+3
-1
One mole of an ideal gas expands adiabatically from an initial state $\left(T_{\mathrm{A}}, V_0\right)$ to final state $\left(T_{\mathrm{f}}, 5 V_0\right)$. Another mole of the same gas expands isothermally from a different initial state $\left(T_{\mathrm{B}}, V_0\right)$ to the same final state $\left(T_{\mathrm{f}}, 5 V_0\right)$. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $T_{\mathrm{A}} / T_{\mathrm{B}}$ ?
A
$5^{\gamma-1}$
B
$5^{1-\gamma}$
C
$5^\gamma$
D
$5^{1+\gamma}$
3
JEE Advanced 2023 Paper 1 Online
+3
-1
Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option.

[Given: Wien's constant as $2.9 \times 10^{-3} \mathrm{~m}-\mathrm{K}$ and $\frac{h c}{e}=1.24 \times 10^{-6} \mathrm{~V}-\mathrm{m}$ ]

List - I List - II
(P) $2000 \mathrm{~K}$ (1) The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work function $4 \mathrm{eV}$.
(Q) $3000 \mathrm{~K}$ (2) The radiation at peak wavelength is visible to human eye.
(R) $5000 \mathrm{~K}$ (3) The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction.
(S) $10000 \mathrm{~K}$ (4) The power emitted per unit area is $1 / 16$ of that emitted by a blackbody at temperature $6000 \mathrm{~K}$.
(5) The radiation at peak emission wavelength can be used to image human bones.
A
$P \rightarrow 3, Q \rightarrow 5, R \rightarrow 2, S \rightarrow 3$
B
$P \rightarrow 3, Q \rightarrow 2, R \rightarrow 4, S \rightarrow 1$
C
$P \rightarrow 3, Q \rightarrow 4, R \rightarrow 2, S \rightarrow 1$
D
$P \rightarrow 1, Q \rightarrow 2, R \rightarrow 5, S \rightarrow 3$
4
JEE Advanced 2022 Paper 1 Online
+3
-1

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?

A
I $\rightarrow$ T, II $\rightarrow$ R, III $\rightarrow$ S, IV $\rightarrow$ Q
B
I $\rightarrow$ S, II $\rightarrow$ P, III $\rightarrow$ T, IV $\rightarrow$ P
C
I $\rightarrow$ P, II $\rightarrow$ R, III $\rightarrow$ T, IV $\rightarrow$ Q
D
I $\rightarrow$ Q, II $\rightarrow$ R, III $\rightarrow$ S, IV $\rightarrow$ T
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