Question:
If the pressure of an ideal gas is doubled and its absolute temperature is halved, the volume will become
If the pressure of an ideal gas is doubled and its absolute temperature is halved, the volume will become
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For fixed amount of gas, use \(\frac{PV}{T}=\text{constant}\). Always use absolute temperature.
Updated On: May 7, 2026
- \(\frac{1}{4}\) of initial volume
- \(\frac{1}{2}\) initial volume
- Same as initial volume
- \(2\) times of initial volume
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The Correct Option is A
Solution and Explanation
Concept:
For an ideal gas:
\[
PV=nRT
\]
For a fixed amount of gas:
\[
\frac{PV}{T}=\text{constant}
\]
Step 1: Let initial pressure, volume, and temperature be: \[ P,\quad V,\quad T \]
Step 2: Final pressure is doubled: \[ P'=2P \] Final absolute temperature is halved: \[ T'=\frac{T}{2} \]
Step 3: Use: \[ \frac{PV}{T}=\frac{P'V'}{T'} \] \[ \frac{PV}{T}=\frac{(2P)V'}{\frac{T}{2}} \] \[ \frac{PV}{T}=\frac{4PV'}{T} \]
Step 4: Cancel \(P\) and \(T\). \[ V=4V' \] \[ V'=\frac{V}{4} \] Therefore, the final volume becomes: \[ \boxed{\frac{1}{4}\text{ of initial volume}} \]
Step 1: Let initial pressure, volume, and temperature be: \[ P,\quad V,\quad T \]
Step 2: Final pressure is doubled: \[ P'=2P \] Final absolute temperature is halved: \[ T'=\frac{T}{2} \]
Step 3: Use: \[ \frac{PV}{T}=\frac{P'V'}{T'} \] \[ \frac{PV}{T}=\frac{(2P)V'}{\frac{T}{2}} \] \[ \frac{PV}{T}=\frac{4PV'}{T} \]
Step 4: Cancel \(P\) and \(T\). \[ V=4V' \] \[ V'=\frac{V}{4} \] Therefore, the final volume becomes: \[ \boxed{\frac{1}{4}\text{ of initial volume}} \]
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