1
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1
Out of Syllabus

A Carnot engine operating between two reservoirs has efficiency $$\frac{1}{3}$$. When the temperature of cold reservoir raised by x, its efficiency decreases to $$\frac{1}{6}$$. The value of x, if the temperature of hot reservoir is $$99^\circ$$C, will be :

A
66 K
B
62 K
C
16.5 K
D
33 K
2
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point '$$\mathrm{K}$$' is :

A
$$-273^{\circ} \mathrm{C}$$
B
$$-373^{\circ} \mathrm{C}$$
C
$$-100^{\circ} \mathrm{C}$$
D
$$-40^{\circ} \mathrm{C}$$
3
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
$$W=R T[2-\sqrt{2}]$$
4
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
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