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Question: At constant temperature on increasing the pressure of a gas by 5% will decrease its volume by...

At constant temperature on increasing the pressure of a gas by 5% will decrease its volume by

A

5%

B

5.26%

C

4.26%

D

4.76%

Answer

4.76%

Explanation

Solution

If P1=PP_{1} = P then P2=P+P_{2} = P +5% of P = 1.05 P

From Boyle’s law PV = constant

∴ V2V1=P1P2=P1.05P=100105\frac{V_{2}}{V_{1}} = \frac{P_{1}}{P_{2}} = \frac{P}{1.05P} = \frac{100}{105}

Fractional change in volume=ΔVV=V2−V1V1= \frac { \Delta V } { V } = \frac { V _ { 2 } - V _ { 1 } } { V _ { 1 } }

=100−105105=−5105= \frac{100 - 105}{105} = - \frac{5}{105}

∴ Percentage change in volume ΔVV×100%=−5105×100%=−4.76%\frac{\Delta V}{V} \times 100\% = - \frac{5}{105} \times 100\% = - 4.76\% i.e. volume decrease by 4.76%.