In a container of ideal gas, the number of molecules is kept constant while the volume is halved and the absolute temperature is doubled. What is the ratio of the new pressure to the original pressure?
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Correct answer
C. 4:1
Principle or equation
For an ideal gas, pressure is proportional to the product of number density and average translational kinetic energy. Average kinetic energy is proportional to absolute temperature. Thus p ∝ (N/V) * T.
Why this answer is correct
Original pressure p1 ∝ (N/V1) * T1. New volume V2 = V1/2, new temperature T2 = 2T1. New pressure p2 ∝ (N/(V1/2)) * (2T1) = 4 * (N/V1) * T1 = 4p1. So the ratio is 4:1.
Example
If a gas initially at 1.0 atm is compressed to half its volume and heated from 300 K to 600 K, the new pressure becomes 4.0 atm.
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