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Thermodynamics

JEE Main level, single correct, medium

99 of 190

Question 99 of 190

Consider two containers $A$ and $B$ containing monoatomic gases at the same Pressure $\left(P\right)$ , Volume $\left(V\right)$ and Temperature $\left(T\right)$ . The gas in $A$ is compressed isothermally to $\dfrac{1}{8}$ of its original volume while the gas in $B$ is compressed adiabatically to $\dfrac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is

Show answer and solution

Answer: (B) $4$

In an isothermal process the temperature is constant.

PV=nRT

So, it can be written that

PV={P}_{A}\left(\dfrac{V}{8}\right) \Rightarrow {P}_{A}=8P

In an adiabatic process,

P{V}^{\gamma }=

constant

\gamma

for monoatomic gas is

\dfrac{5}{3}

So, it can be written

\dfrac{{P}_{B}}{P}={\left(\dfrac{V}{\dfrac{V}{8}}\right)}^{\dfrac{5}{3}} \Rightarrow {P}_{B}=32P

Thus, the ratio of the pressures is

\dfrac{{P}_{B}}{{P}_{A}}=\dfrac{32P}{8P}=4

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JEE Main 2025 Apr 2 Shift 1 question paper

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