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JIPMER 2016

Exam: JIPMER
Year: 2016
Subject: Physics
Chapter: Kinetic Theory of Gases

JIPMER 2016 · Physics · Kinetic Theory of Gases

Two different isotherms representing the relationship between...

Two different isotherms representing the relationship between pressure

p

and volume

V

at a given temperature of the same ideal gas are shown for masses

m_1

and

m_2

, then

Two different isotherms representing the relationship between pressure p and volume V at a given temperature of the

Options

ANothing can be predicted
B $m_1 \lt m_2$
C $m_1=m_2$
D $m_1 \gt m_2$

Correct answer

B. $m_1 \lt m_2$

Step-by-step solution

\because \quad p V=n R T=\frac{m}{M} R T

For

m_1, \quad p=\frac{m_1}{M} \cdot \frac{R T}{V_1}

...(i) For

m_2, \quad p=\frac{m_2}{M} \cdot \frac{R T}{V_2}

....(ii) From Eqs. (i) and (ii), we get

\frac{m_1}{M} \cdot \frac{R T}{V_1}=\frac{m_2}{M} \cdot \frac{R T}{V_2} \Rightarrow \frac{m_1}{V_1}=\frac{m_2}{V_2}

\begin{aligned} & \text{ Thus, } \quad V \propto m \\ & \because \quad V_2 > V_1 \\ & \therefore \quad m_2 > m_1 \\ & \end{aligned}

$$

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