Verified Solution • 2025–26 Session moderate

QJEEM23Phba3f: JEE Main 2023 Physics - Class 11 JEEM23Phba3f Solution: The pressure and temperature ( relationship of an ideal gas…

The pressure $(\mathrm{P})$ and temperature ( $\mathrm{T})$ relationship of an ideal gas obeys the equation $\mathrm{PT}^{2}=$ constant. The volume expansion coefficient of the gas will be :

Multiple Choice Options

A $3 T^{2}$
B $\frac{3}{T^2}$
C $\frac{3}{T^3}$
D $\frac{3}{T}$

Step-by-Step Verified Solution

$PT^2$ = constant

From $PV = nRT \Rightarrow {{{T^3}} \over V} =$ constant

${T^3} \propto V$ ..... (1)

$3{T^2}dT \propto dV$ ..... (2)

From (1) and (2)

${{3dT} \over T} = {{dV} \over V}$

$\therefore$ $\gamma = {1 \over V}{{dV} \over {dT}} = {3 \over T}$

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