If the pressure on an enclosed gas is doubled and its temperature rises from 27ºC to 127ºC, then its volume will

Analyze the question: A fixed mass of gas has its pressure doubled and its temperature raised from 27°C to 127°C. We need to find how the volume changes.

Concept: For a fixed mass of gas, the combined gas law applies:

P₁V₁/T₁ = P₂V₂/T₂

Temperature must be in kelvin: T = °C + 273.

Solution:

• T₁ = 27 + 273 = 300 K
• T₂ = 127 + 273 = 400 K
• P₂ = 2P₁

Substitute:

P₁V₁/300 = (2P₁)V₂/400

Cancel P₁:

V₁/300 = 2V₂/400

V₂ = (400/600)V₁ = (2/3)V₁

So the new volume is 2/3 of the original. The change in volume is:

V₁ − V₂ = V₁ − (2/3)V₁ = (1/3)V₁

The volume decreases by 1/3 of its original value.

Tip: Be careful about the difference between "becomes 2/3 of the original" and "decreases by 2/3". The first describes the final volume, while the second describes the amount lost. Always compute the final volume first, then subtract it from the original to find the change. Also, always convert to kelvin before using any gas law.