Thermal Properties of Matter

JEE Main level, single correct, medium

27 of 126

Question 27 of 126

An ideal gas is expanding such that PT3=P{T}^{3}= constant. The coefficient of volume expansion of the gas is:

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Answer: (D) 4T\dfrac{4}{T}

γ=1VdVdt\gamma =\dfrac{1}{V}\dfrac{dV}{dt}
PT3=P{T}^{3}= constant
TVT3=\dfrac{T}{V}{T}^{3}= Constant
T4V−1=C{T}^{4}{V}^{-1}=C
V−1(4T3dT)+T4(−1V2dV)=0{V}^{-1}\left(4{T}^{3}dT\right)+{T}^{4}\left(\dfrac{-1}{{V}^{2}}dV\right)=0
dVdT=4T3/VT4/V2=4VT∴γ=4T\dfrac{dV}{dT}=\dfrac{4{T}^{3}/V}{{T}^{4}/{V}^{2}}=\dfrac{4V}{T}∴\gamma =\dfrac{4}{T}

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