A box containing N molecules of a perfect gas at temperature {T_1} and pressure {P_1}. The number of molecules in the box is doubled keeping

Q: A box containing $N$ molecules of a perfect gas at temperature ${T_1}$ and pressure ${P_1}$. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is ${P_2}$ and temperature ${T_2}$, then

b ${E_{total}} = \frac{f}{2}NkT$ $\Rightarrow$ $T \propto \frac{1}{N}$ [$\because$ ${E_{total}} , f, k =$ determinant] $\Rightarrow$ $\frac{{{T_2}}}{{{T_1}}} = \frac{{{N_1}}}{{{N_2}}} = \frac{1}{2}$ $\Rightarrow$ ${T_2} = \frac{{{T_1}}}{2}$ and $PV = NkT$ $\Rightarrow$ $P \propto NT$ $\Rightarrow$ $\frac{{{P_1}}}{{{P_2}}} = \frac{{{N_1}}}{{{N_2}}}.\frac{{{T_1}}}{{{T_2}}} = \frac{1}{2} \times \frac{2}{1} = \frac{1}{1}$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

A box containing $N$ molecules of a perfect gas at temperature ${T_1}$ and pressure ${P_1}$. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is ${P_2}$ and temperature ${T_2}$, then

A${P_2} = {P_1},\;{T_2} = {T_1}$
B${P_2} = {P_1},\;{T_2} = \frac{{{T_1}}}{2}$
C${P_2} = 2{P_1},\;{T_2} = {T_1}$
D${P_2} = 2{P_1},\;{T_2} = \frac{{{T_1}}}{2}$

Medium

STD 11 Science
JEE
STD 11 - 12 . kinetic theory of gases
Physics

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