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AIIMS 2009
Exam
AIIMS
Year
2009
Subject
Chemistry
Chapter
States of Matter

AIIMS 2009 · Chemistry · States of Matter

The variation of volume V , with temperature T , keeping pressure...

The variation of volume VV, with temperature TT, keeping pressure constant is called the coefficient of thermal expansion (α)(\alpha) of a gas. i.e., α=1V(∂V∂T)P\alpha=\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_P. For an ideal gas α\alpha is equal to

Options

  1. ATT
  2. B1/T1 / T
  3. CPP
  4. D1/P1 / P.

Correct answer

B. 1/T1 / T

Step-by-step solution

For nn moles of an ideal gas PV=nRTorV=nRTPP V=n R T or V=n \frac{R T}{P} Differentiating with respect to TT at constant PP, we have (∂V∂T)P=nRP=VTα=1V(∂V∂T)P=1V×VT=1T\begin{aligned} & \left(\frac{\partial V}{\partial T}\right)_P=\frac{n R}{P}=\frac{V}{T} \\ & \alpha=\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_P=\frac{1}{V} \times \frac{V}{T}=\frac{1}{T}\end{aligned}
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