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PART - 2 CH - 12 Kinetic Theory — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 12 Kinetic Theory2 Marks
Question
N molecules of a gas are in a container at absolute temperature T. Now the number of molecules is doubled and the total energy of the gas in the container remains the same, then find the absolute temperature of the gas.
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Answer

$ E_1=N$ Eenrgy of $N$ molecules at $T K$
$\begin{array}{c}E_1=\frac{3}{2} NkT\quad\quad\ldots\ldots (1) \\\begin{array}{c}E_2=\text { Energy of } 2 N \text { molecules at } T^{\prime} K \left( T ^{\prime} K , 2 N\right. ~\text {molecules}) \\\end{array}\end{array}$
$\begin{aligned}& =\frac{3}{2} \times 2 NkT^{\prime} \\\text { Given : } \quad E_1 & =E_2 \\\frac{3}{2} NkT & =\frac{3}{2} \times 2 NkT^{\prime} \\\Rightarrow \quad T & =2 T^{\prime} \\\therefore \quad T^{\prime} & =\frac{1}{2} T\end{aligned}$
Abolsute temperature of gas $=\frac{1}{2} TK$

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