1
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.
2
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

Which statements are correct about degrees of freedom ?

(A) A molecule with n degrees of freedom has n$$^{2}$$ different ways of storing energy.

(B) Each degree of freedom is associated with $$\frac{1}{2}$$ RT average energy per mole.

(C) A monatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom.

(D) $$\mathrm{CH}_{4}$$ has a total of 6 degrees of freedom.

Choose the correct answer from the options given below :

A
(B) and (C) only
B
(B) and (D) only
C
(A) and (B) only
D
(C) and (D) only
3
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

If $$K_{1}$$ and $$K_{2}$$ are the thermal conductivities, $$L_{1}$$ and $$L_{2}$$ are the lengths and $$A_{1}$$ and $$A_{2}$$ are the cross sectional areas of steel and copper rods respectively such that $$\frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2$$. Then, for the arrangement as shown in the figure, the value of temperature $$\mathrm{T}$$ of the steel - copper junction in the steady state will be:

A
$$18^{\circ} \mathrm{C}$$
B
$$14^{\circ} \mathrm{C}$$
C
$$45^{\circ} \mathrm{C}$$
D
$$150^{\circ} \mathrm{C}$$
4
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice.

B. Two bodies $$P$$ and $$Q$$ having equal surface areas are maintained at temperature $$10^{\circ} \mathrm{C}$$ and $$20^{\circ} \mathrm{C}$$. The thermal radiation emitted in a given time by $$\mathrm{P}$$ and $$\mathrm{Q}$$ are in the ratio $$1: 1.15$$.

C. A Carnot Engine working between $$100 \mathrm{~K}$$ and $$400 \mathrm{~K}$$ has an efficiency of $$75 \%$$.

D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below :

A
A, B, C only
B
A, B only
C
A, C only
D
B, C, D only
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