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Difficulty: MediumBoyle's Law and Pressure-Volume Relationship

Under isothermal conditions, reducing the volume of a fixed mass of an ideal gas to one-third of its initial volume results in a threefold increase in its pressure. State whether this statement is True or False.

Answer: Answer

Answer

The statement is True.
Boyle's law dictates an inverse relationship between gas pressure and volume at constant temperature (P1V1=P2V2P_1V_1 = P_2V_2). If volume is reduced by a factor of 3, pressure must increase by a factor of 3 to keep the product of pressure and volume constant.

Step-by-Step Solution

1
State Boyle's Law equation for isothermal processes
P1V1=P2V2P_1 V_1 = P_2 V_2
Temperature and mass are held constant.
2
Substitute the new volume condition V2=13V1V_2 = \frac{1}{3} V_1 into the equation
P1V1=P2(13V1)P_1 V_1 = P_2 \left(\frac{1}{3} V_1\right)
The final volume is one-third of the initial volume.
3
Solve for the final pressure P2P_2
P2=3P1P_2 = 3 P_1
Dividing both sides by V1V_1 and multiplying by 3 yields a final pressure three times the initial pressure.

Key Concept

Inverse proportional relationship between pressure and volume in Boyle's Law (P∝1VP \propto \frac{1}{V} at constant TT).
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Topics

Boyle's Law and Pressure-Volume Relationship

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