1
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

Given below are two statements :

Statement I : When $$\mu$$ amount of an ideal gas undergoes adiabatic change from state (P1, V1, T1) to state (P2, V2, T2), then work done is $$W = {{\mu R({T_2} - {T_1})} \over {1 - \gamma }}$$, where $$\gamma = {{{C_p}} \over {{C_v}}}$$ and R = universal gas constant.

Statement II : In the above case, when work is done on the gas, the temperature of the gas would rise.

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

For a perfect gas, two pressures P1 and P2 are shown in figure. The graph shows :

A
P1 > P2
B
P1 < P2
C
P1 = P2
D
Insufficient data to draw any conclusion
3
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

According to kinetic theory of gases,

A. The motion of the gas molecules freezes at 0$$^\circ$$C.

B. The mean free path of gas molecules decreases if the density of molecules is increased.

C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.

D. Average kinetic energy per molecule per degree of freedom is $${3 \over 2}{k_B}T$$ (for monoatomic gases).

Choose the most appropriate answer from the options given below :

A
A and C only
B
B and C only
C
A and B only
D
C and D only
4
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is :

(Given : initial temperature of the bullet = 127$$^\circ$$C, Melting point of the bullet = 327$$^\circ$$C, Latent heat of fusion of lead = 2.5 $$\times$$ 104 J kg$$-$$1, Specific heat capacity of lead = 125 J/kg K)

A
125 ms$$-$$1
B
500 ms$$-$$1
C
250 ms$$-$$1
D
600 ms$$-$$1
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