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NEET PHYSICSKinetic TheoryMedium

Question

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\%.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Kinetic Theory. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSKinetic Theoryconstanttemperatureincreasingpressurevolume

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