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NEET PHYSICSMedium

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

A

5%

B

5.26%

C

4.26%

D

4.76%

Step-by-Step Solution

According to Boyle's Law (derived from the Ideal Gas Equation pV=nRTpV = nRT at constant temperature ), pressure is inversely proportional to volume (P1/VP \propto 1/V or P1V1=P2V2P_1V_1 = P_2V_2). Let initial pressure be PP and initial volume be VV. New pressure P=P+0.05P=1.05PP' = P + 0.05P = 1.05P. Using the relation PV=PVPV = P'V', we get: V=PVP=PV1.05P=V1.05V' = \frac{PV}{P'} = \frac{PV}{1.05P} = \frac{V}{1.05}. The decrease in volume is ΔV=VV=VV1.05=V(111.05)=V(0.051.05)\Delta V = V - V' = V - \frac{V}{1.05} = V(1 - \frac{1}{1.05}) = V(\frac{0.05}{1.05}). The percentage decrease is ΔVV×100=0.051.05×1004.76%\frac{\Delta V}{V} \times 100 = \frac{0.05}{1.05} \times 100 \approx 4.76\%.

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