1
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. The work done by the gas in the process is $$\left(\mathrm{given}, \gamma=\frac{3}{2}\right)$$ :

A
$$W=T R[\sqrt{2}-2]$$
B
$$W=\frac{T}{R}[\sqrt{2}-2]$$
C
$$W=\frac{R}{T}[2-\sqrt{2}]$$
D
$$W=R T[2-\sqrt{2}]$$
2
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

$$\left(P+\frac{a}{V^{2}}\right)(V-b)=R T$$ represents the equation of state of some gases. Where $$P$$ is the pressure, $$V$$ is the volume, $$T$$ is the temperature and $$a, b, R$$ are the constants. The physical quantity, which has dimensional formula as that of $$\frac{b^{2}}{a}$$, will be:

A
Energy density
B
Bulk modulus
C
Modulus of rigidity
D
Compressibility
3
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1
Heat energy of $735 \mathrm{~J}$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be :
A
$572 \mathrm{~J}$
B
$441 \mathrm{~J}$
C
$525 \mathrm{~J}$
D
$735 \mathrm{~J}$
4
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1
A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$. Then the ratio of $\frac{\mathrm{Cp}}{\mathrm{Cv}}$ will be.
A
$\frac{3}{1}$
B
$\frac{4}{3}$
C
$\frac{1}{2}$
D
$\frac{3}{2}$
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