Ideal Gas Molecules
5 marks · NormalA fixed mass of gas in a metal cylinder is at a pressure of 120 kPa and a temperature of 300 K. The gas is then compressed while being heated, so that its temperature rises to 360 K and its volume halves.
Write down the gas law equation that links pressure, volume, and temperature for a fixed mass of gas.
Calculate the final pressure of the gas, in kPa.
Explain why the pressure in the cylinder increases, even though the gas is heated.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) p1 V1 / T1 = p2 V2 / T2
(b) 288 kPa · must show substitution and correct final answer
(c) The pressure increases because the volume decreases by a larger factor than the temperature increases. Compressing the gas has a stronger effect on increasing pressure than heating it (the halving of volume doubles the pressure, while the rise in temperature increases it by a smaller fraction). · must show volume change effect larger than temperature change
Common mistakes: Not halving volume correctly; Using Celsius instead of Kelvin
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Gives correct gas law: p1V1 / T1 = p2V2 / T2 (or equivalent).
M1 (b) · 1 mark · Writes and substitutes values into the gas law correctly.
A1 (b) · 1 mark · Rearranges and solves for p2.
A2 (b) · 1 mark · Evaluates and states final answer (288 kPa; units required).
B2 (c) · 1 mark · Explains that the decrease in volume has a greater effect on pressure than the increase in temperature.
Worked solution
(a) The gas law for a fixed mass is:
(b) p1 = 120 kPa, T1 = 300 K, V1 = V; V2 = 0.5 V, T2 = 360 K
Rearrange for :
(c) Compressing the gas (halving the volume) increases the pressure more than heating does. The reduction in space for particles to move gives more collisions per second, increasing pressure more than the higher temperature.