1
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1 Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $$1: 4$$, then

A. The r.m.s. velocity of gas molecules in two vessels will be the same.

B. The ratio of pressure in these vessels will be $$1: 4$$.

C. The ratio of pressure will be $$1: 1$$.

D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $$1: 4$$.

Choose the correct answer from the options given below :

A
A and C only
B
B and D only
C
A and B only
D
C and D only
2
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1 An ice cube of dimensions $$60 \mathrm{~cm} \times 50 \mathrm{~cm} \times 20 \mathrm{~cm}$$ is placed in an insulation box of wall thickness $$1 \mathrm{~cm}$$. The box keeping the ice cube at $$0^{\circ} \mathrm{C}$$ of temperature is brought to a room of temperature $$40^{\circ} \mathrm{C}$$. The rate of melting of ice is approximately :

(Latent heat of fusion of ice is $$3.4 \times 10^{5} \mathrm{~J} \mathrm{~kg}^{-1}$$ and thermal conducting of insulation wall is $$0.05 \,\mathrm{Wm}^{-1 \circ} \mathrm{C}^{-1}$$ )

A
$$61 \times 10^{-3} \mathrm{~kg} \mathrm{~s}^{-1}$$
B
$$61 \times 10^{-5} \mathrm{~kg} \mathrm{~s}^{-1}$$
C
$$208 \mathrm{~kg} \mathrm{~s}^{-1}$$
D
$$30 \times 10^{-5} \mathrm{~kg} \mathrm{~s}^{-1}$$
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1 A gas has $$n$$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :

A
$$\frac{n}{n+2}$$
B
$$\frac{n+2}{n}$$
C
$$\frac{n}{2n+2}$$
D
$$\frac{n}{n-2}$$
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1 7 mol of a certain monoatomic ideal gas undergoes a temperature increase of $$40 \mathrm{~K}$$ at constant pressure. The increase in the internal energy of the gas in this process is :

(Given $$\mathrm{R}=8.3 \,\mathrm{JK}^{-1} \mathrm{~mol}^{-1}$$ )

A
5810 J
B
3486 J
C
11620 J
D
6972 J
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