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JEE Advanced 2008Paper 1

Exam: JEE Advanced
Year: 2008
Paper: Paper 1
Subject: Physics
Chapter: Thermodynamics

JEE Advanced 2008 · Paper 1 · Physics · Thermodynamics

An ideal gas is expanding such that p T^2= constant. The...

An ideal gas is expanding such that

p T^2=

constant. The coefficient of volume expansion of the gas is

Options

A $\frac{1}{T}$
B $\frac{2}{T}$
C $\frac{3}{T}$
D $\frac{4}{T}$

Correct answer

C. $\frac{3}{T}$

Step-by-step solution

p T^2=

constant

\begin{array}{ll}\therefore \quad & \left(\frac{n R T}{V}\right) T^2=\text { constant } \\ \text { or } \quad T^3 V^{-1}=\text { constant }\end{array}

Differentiating the equation, we get

\frac{3 T^2}{V} \cdot d T-\frac{T^3}{V^2} \cdot d V=0

or

3 \cdot d T=\frac{T}{V} \cdot d V

From the equation,

d V=V \gamma \cdot d T

\gamma

= coefficient of volume expansion of gas

=\frac{d V}{V \cdot d T}

From Eq. (i)

\gamma=\frac{d V}{V \cdot d T}=\frac{3}{T}

\therefore

correct answer is (c).

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