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Question

By how much should the pressure be increased in order to decrease the volume of a gas by 5% at a constant temperature?

A
5%
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B
5.26%
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C
10%
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D
4.26%
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Solution

The correct option is B 5.26%
Boyle's law states that at constant temperature, the product of pressure and volume is constant.

Assume the pressure and the volume of the gas at tnitial conditions to be P1,V1
and the pressure and the volume of the gas at final condition to be P2,V2

The final volume is decreased by 5% and therefore, V2=0.95V1

We can calculate P2 from the equation,
P1V1 = P2V2

Hence P2=P1(V10.95V1)
= P2=1.0526P1

Now increase in pressure = P2P1
= 0.526

In terms of percentage, the same can be expressed as 5.26%

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