An ideal gas is trapped in a metal cylinder by a free-moving piston and is at equilibrium in a room at 25°C.
The piston is pulled slowly to the right so that the volume of the trapped gas increases isothermally. The piston is now fixed in position.
The metal cylinder is then placed in a location where thermal energy is transferred from the trapped gas until the pressure of the gas is halved.
To the nearest degree Celsius, what is the final temperature of the gas?
A) −149°C
B) 13°C
C) 50°C
D) 25°C
E) −124°C
IMAT 2023 · Question 57
Q57 - Ideal gas laws
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The correct answer is E) −124°C.
The first step is isothermal, so the gas is still at 25 °C = 298 K afterwards. How much the volume changed doesn't matter.
Then the piston is fixed, so the volume is constant and pressure is proportional to temperature in kelvin. Halving the pressure halves the temperature: 298/2 = 149 K, which is −124 °C.
−149 °C is what you get if you forget to convert 149 K back to Celsius.
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