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Question: A container has N molecules at absolute temperature T. If the number of molecules is doubled but kin...

A container has N molecules at absolute temperature T. If the number of molecules is doubled but kinetic energy in the box remains the same as before, the absolute temperature of the gas is –

A

T

B

T/2

C

2T

D

Zero

Answer

T/2

Explanation

Solution

Apply conservation of energy

N[32KT]=2N[32KT′]⇒T′=T2N\left\lbrack \frac{3}{2}KT \right\rbrack = 2N\left\lbrack \frac{3}{2}KT' \right\rbrack \Rightarrow \begin{matrix} T^{'} = \frac{T}{2} \end{matrix}