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Standard XII

Physics

Degree of Freedom

A certain amo...

Question

A certain amount of an ideal gas is initially at a pressure $p_{1}$ and temperature $T_{1}$ . First, it undergoes a constant pressure process 1-2 such that $T_{2} = 3 T_{1}$ /4. Then, it undergoes a constant volume process 2-3 such that $T_{3} = T_{1} / 2$ . The ratio of the final volume to the initial volume of the ideal gas is

0.25

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0.75

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1.0

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1.5

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Solution

The correct option is B 0.75

Process 1 - 2: At p=C

$T_{2} = \frac{3 T_{1}}{4}$ . (given condition)

(or). $\frac{T_{2}}{T_{1}} = \frac{3}{4}$

According to Charles's law

$\frac{V_{2}}{V_{1}}$ = $\frac{T_{2}}{T_{1}} = \frac{3}{4}$

Process 2 - 3: At V = C

$T_{3} = \frac{T_{1}}{2}$ given condition

$\frac{F i n a l v o l u m e}{I n i t i a l v o l u m e}$ = $\frac{V_{3}}{V_{1}} = \frac{V_{2}}{V_{1}}$ = $\frac{T_{2}}{T_{1}}$ $∵$ $V_{3} = V_{2}$

= $\frac{3}{4} = 0.75$

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A certain amount of an ideal gas is initially at a pressure p1and temperature T1. First, it undergoes a constant pressure process 1-2 such that T2=3T1/4. Then, it undergoes a constant volume process 2-3 such that T3=T1/2. The ratio of the final volume to the initial volume of the ideal gas is

The correct option is B 0.75 Process 1 - 2: At p=C T2=3T14. (given condition) (or). T2T1=34 According to Charles's law V2V1 = T2T1=34 Process 2 - 3: At V = C T3=T12 given condition FinalvolumeInitialvolume = V3V1=V2V1 = T2T1 ∵ V3=V2 = 34=0.75