1
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1

Two vessels $$A$$ and $$B$$ are of the same size and are at same temperature. A contains $$1 \mathrm{~g}$$ of hydrogen and $$B$$ contains $$1 \mathrm{~g}$$ of oxygen. $$\mathrm{P}_{\mathrm{A}}$$ and $$\mathrm{P}_{\mathrm{B}}$$ are the pressures of the gases in $$\mathrm{A}$$ and $$\mathrm{B}$$ respectively, then $$\frac{P_A}{P_B}$$ is:

A
4
B
32
C
8
D
16
2
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $$\frac{\mathrm{Cp}}{\mathrm{Cv}}$$ for the gas is :

A
$$\frac{7}{5}$$
B
$$\frac{3}{2}$$
C
$$\frac{9}{7}$$
D
$$\frac{5}{3}$$
3
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

The equation of state of a real gas is given by $$\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$$, where $$\mathrm{P}, \mathrm{V}$$ and $$\mathrm{T}$$ are pressure, volume and temperature respectively and $$\mathrm{R}$$ is the universal gas constant. The dimensions of $$\frac{\mathrm{a}}{\mathrm{b}^2}$$ is similar to that of :

A
P
B
RT
C
PV
D
R
4
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

The total kinetic energy of 1 mole of oxygen at $$27^{\circ} \mathrm{C}$$ is : [Use universal gas constant $$(R)=8.31 \mathrm{~J} /$$ mole K]

A
6232.5 J
B
5670.5 J
C
6845.5 J
D
5942.0 J
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