Question:
A gas at pressure \( P \), volume \( V \), and temperature \( T \). If pressure is doubled and temperature is halved, the new volume is:
A gas at pressure \( P \), volume \( V \), and temperature \( T \). If pressure is doubled and temperature is halved, the new volume is:
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When multiple variables change, track them one by one. Doubling the pressure tends to compress the gas to half its volume (\( V/2 \)). Halving the temperature compresses it even further by half again. So, \( 1/2 \times 1/2 = 1/4 \).
Updated On: Jun 3, 2026
- \( V \)
- \( V/2 \)
- \( V/4 \)
- \( 2V \)
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The Correct Option is C
Solution and Explanation
Concept:
This problem is solved using the Combined Gas Law, which relates the pressure, volume, and temperature of a fixed amount of gas.
• Combined Gas Law Formula: \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \)
• \( P \): Pressure.
• \( V \): Volume.
• \( T \): Absolute temperature (must be in Kelvin).
Step 1: Identifying the initial and final states.
Initial State: \[ P_1 = P, \quad V_1 = V, \quad T_1 = T \] Final State (according to conditions): \[ P_2 = 2P \quad (\text{doubled}) \] \[ T_2 = T/2 \quad (\text{halved}) \] Let the new volume be \( V_2 \).
Step 2: Substituting values into the gas law equation.
\[ \frac{P \cdot V}{T} = \frac{(2P) \cdot V_2}{(T/2)} \] To simplify the right side, recall that dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{PV}{T} = \frac{2P \cdot V_2 \cdot 2}{T} = \frac{4P \cdot V_2}{T} \]
Step 3: Solving for \( V_2 \).
Cancel \( P \) and \( T \) from both sides of the equation: \[ V = 4V_2 \] \[ V_2 = \frac{V}{4} \]
• Combined Gas Law Formula: \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \)
• \( P \): Pressure.
• \( V \): Volume.
• \( T \): Absolute temperature (must be in Kelvin).
Step 1: Identifying the initial and final states.
Initial State: \[ P_1 = P, \quad V_1 = V, \quad T_1 = T \] Final State (according to conditions): \[ P_2 = 2P \quad (\text{doubled}) \] \[ T_2 = T/2 \quad (\text{halved}) \] Let the new volume be \( V_2 \).
Step 2: Substituting values into the gas law equation.
\[ \frac{P \cdot V}{T} = \frac{(2P) \cdot V_2}{(T/2)} \] To simplify the right side, recall that dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{PV}{T} = \frac{2P \cdot V_2 \cdot 2}{T} = \frac{4P \cdot V_2}{T} \]
Step 3: Solving for \( V_2 \).
Cancel \( P \) and \( T \) from both sides of the equation: \[ V = 4V_2 \] \[ V_2 = \frac{V}{4} \]
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