JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Heat & Thermodynamics

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at

2 7^{\circ} C

(A) $122 7^{\circ} C$
(B) $92 7^{\circ} C$
(C) $32 7^{\circ} C$ ✓ Correct
(D) $62 7^{\circ} C$

Answer: (C)

Solution

The kinetic energy of gas molecules is proportional to absolute temperature:

K E = \frac{f}{2} k T

. If the kinetic energy doubles, the temperature also doubles. Initial temperature

T_{1} = 2 7^{\circ}

C = 300 K. For the kinetic energy to double:

\frac{K _{2}}{K _{1}} = \frac{T _{2}}{T _{1}} = 2

. Therefore

T_{2} = 2 \times 300 = 600

K =

32 7^{\circ}

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Single correct option

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