1
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

A vessel contains $$14 \mathrm{~g}$$ of nitrogen gas at a temperature of $$27^{\circ} \mathrm{C}$$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be :

Take $$\mathrm{R}=8.32 \mathrm{~J} \mathrm{~mol}^{-1} \,\mathrm{k}^{-1}$$.

A
2229 J
B
5616 J
C
9360 J
D
13,104 J
2
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1
Out of Syllabus

A Carnot engine has efficiency of $$50 \%$$. If the temperature of sink is reduced by $$40^{\circ} \mathrm{C}$$, its efficiency increases by $$30 \%$$. The temperature of the source will be:

A
166.7 K
B
255.1 K
C
266.7 K
D
367.7 K
3
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

Given below are two statements :

Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.

Statement II : The rms speed of oxygen molecules in a gas is $$v$$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $$2 v$$.

In the light of the above statements, choose the correct answer from the options given below :

A
Both Statement I and Statement II are true
B
Both Statement I and Statement II are false
C
Statement I is true but Statement II is false
D
Statement I is false but Statement II is true
4
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1
Out of Syllabus

In $$1^{\text {st }}$$ case, Carnot engine operates between temperatures $$300 \mathrm{~K}$$ and $$100 \mathrm{~K}$$. In $$2^{\text {nd }}$$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in $$2^{\text {nd }}$$ case) will be :

A
same as the $$1^{\text {st }}$$ case.
B
always greater than the $$1^{\text {st }}$$ case.
C
always less than the $$1^{\text {st }}$$ case.
D
may increase or decrease with respect to the $$1^{\text {st }}$$ case.
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