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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Thermal Properties of Matter

NTA Abhyas 2020 · Physics · Thermal Properties of Matter

An ideal gas is expanding such as PT^ 2 = constant . The...

An ideal gas is expanding such as PT2=constantPT^{2} = constant. The coefficient of volume expansion of the gas is

Options

  1. A1T\dfrac{1}{T}
  2. B2T\dfrac{2}{T}
  3. C3T\dfrac{3}{T}
  4. D4T\dfrac{4}{T}

Correct answer

C. 3T\dfrac{3}{T}

Step-by-step solution

PT^{2} = constant</p><p>(nRTV)T2=nRT3V−1=constant</p><p>\left(\dfrac{nRT}{V}\right)T^{2} = nRT^{3}V^{- 1} = constant

Differentiating the equation, we get

3nRVT2dT−nRT3dVV2=0\dfrac{3nR}{V}T^{2}dT - nRT^{3}\dfrac{dV}{V2} = 0

⇒γ=1VdVdT=3T⇒ \gamma = \dfrac{1}{V}\dfrac{dV}{dT} = \dfrac{3}{T}

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