1
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
The entropy of any system is given by
$$S = {\alpha ^2}\beta \ln \left[ {{{\mu kR} \over {J{\beta ^2}}} + 3} \right]$$ where $$\alpha$$ and $$\beta$$ are the constants. $$\mu$$, J, k and R are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively.
[Take $$S = {{dQ} \over T}$$]
Choose the incorrect option from the following :
A
$$\alpha$$ and J have the same dimensions.
B
S and $$\alpha$$ have different dimensions
C
S, $$\beta$$, k and $$\mu$$R have the same dimensions
D
$$\alpha$$ and k have the same dimensions
2
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be :

(Molecular weight of oxygen is 32g/mol; R = 8.3 J K$$-$$1 mol$$-$$1)
A
$$\sqrt {{{3\pi } \over 8}}$$
B
$$\sqrt {{3 \over 3}}$$
C
$$\sqrt {{8 \over 3}}$$
D
$$\sqrt {{{8\pi } \over 3}}$$
3
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $$\gamma$$ is the ratio of specific heats) :
A
$$- {1 \over \gamma }{{dV} \over V}$$
B
$$- \gamma {V \over {dV}}$$
C
$$- \gamma {{dV} \over V}$$
D
$${{dV} \over V}$$
4
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S1 and that of the other part is S2. Given that S1 > S2. If the piston is removed then the total entropy of the system will be :
A
S1 $$-$$ S2
B
$${{{S_1}} \over {{S_2}}}$$
C
S1 $$\times$$ S2
D
S1 + S2
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