Question:
Two gases \(A\) and \(B\) are initially at same pressure, volume and temperature. If \(A\) is compressed isothermally and \(B\) adiabatically to half of the initial volume, then the final pressure of \(A\)
Two gases \(A\) and \(B\) are initially at same pressure, volume and temperature. If \(A\) is compressed isothermally and \(B\) adiabatically to half of the initial volume, then the final pressure of \(A\)
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Adiabatic compression increases pressure more rapidly than isothermal compression because temperature also rises during compression.
Updated On: Jun 17, 2026
- greater than the final pressure of \(B\)
- equal to the final pressure of \(B\)
- less than the final pressure of \(B\)
- twice the final pressure of \(B\)
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The Correct Option is C
Solution and Explanation
Concept:
For isothermal process:
\[
PV=\text{constant}
\]
For adiabatic process:
\[
PV^\gamma=\text{constant}
\]
Since \(\gamma>1\), pressure rises faster in adiabatic compression.
Step 1: Pressure in isothermal compression. \[ P_A V_i=P'_A \frac{V_i}{2} \] \[ P'_A=2P \]
Step 2: Pressure in adiabatic compression. \[ PV^\gamma=P'_B\left(\frac V2\right)^\gamma \] \[ P'_B=P2^\gamma \] Since: \[ 2^\gamma>2 \] therefore, \[ P'_B>P'_A \] Thus pressure of gas \(A\) is less. Hence, \[ \boxed{\text{Final pressure of A is less than that of B}} \]
Step 1: Pressure in isothermal compression. \[ P_A V_i=P'_A \frac{V_i}{2} \] \[ P'_A=2P \]
Step 2: Pressure in adiabatic compression. \[ PV^\gamma=P'_B\left(\frac V2\right)^\gamma \] \[ P'_B=P2^\gamma \] Since: \[ 2^\gamma>2 \] therefore, \[ P'_B>P'_A \] Thus pressure of gas \(A\) is less. Hence, \[ \boxed{\text{Final pressure of A is less than that of B}} \]
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