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JEE Main 202127 AugustMorning Shift
Exam
JEE Main
Year
2021
Date
27 August
Shift
Morning Shift
Subject
Physics
Chapter
Thermal Properties of Matter

JEE Main 2021 · 27 August · Morning Shift · Physics · Thermal Properties of Matter

An ideal gas is expanding such that P T ^ 3 = constant. The...

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

Options

  1. A2T\dfrac{2}{T}
  2. B3T\dfrac{3}{T}
  3. C1T\dfrac{1}{T}
  4. D4T\dfrac{4}{T}

Correct answer

D. 4T\dfrac{4}{T}

Step-by-step solution

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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