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Physics Question 33 – JEE-MAIN 2025

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A monatomic gas having γ=53 is stored in a thermally insulated container and the gas is suddenly compressed to (18)th of its initial volume. The ratio of final pressure and initial pressure is: (γ is the ratio of specific heats of the gas at constant pressure and at constant volume)

The problem describes a gas in a thermally insulated container undergoing sudden compression, which indicates an adiabatic process.

Step 1: Identify the process and relevant equation✦ Active

The gas is in a thermally insulated container and compressed suddenly, indicating an adiabatic process. For an adiabatic process, the relation between pressure (P) and volume (V) is PVγ=constant.

PiViγ=PfVfγ
Step 2: Set up the ratio of pressures○ Expand

Rearrange the adiabatic equation to find the ratio of final to initial pressure:

PfPi=(ViVf)γ
Step 3: Substitute given values and calculate○ Expand

Given γ=53 and Vf=18Vi, which means ViVf=8. Substitute these into the ratio equation:

PfPi=(8)53=((8)13)5=(2)5=32
💡 Teacher's Secret Hint

Remember that (a1/n)m=am/n.

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