Answers · Gas pressure and temperature

Gas pressure and temperature — final check key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. GK1 · Final check

Model answer. (a) At B the air has a third of the volume it had at A. The same particles, at the same temperature, move at the same speed, but they are more crowded, so each square centimetre of the walls is hit more often each second. More hits give a bigger force on each unit of area: a higher pressure. (b) At A, pV = 100 kPa × 60 cm³ = 6000 kPa cm³; at B, pV = 300 kPa × 20 cm³ = 6000 kPa cm³. The product is the same. (c) V = 6000 kPa cm³ ÷ 150 kPa = 40 cm³. (d) A straight line through the origin: p is proportional to 1/V. (e) The mass of the gas must stay fixed, and its temperature must stay constant.

A full answer includes

(a) At B the same particles have a third of the space; at the same speed they hit each square centimetre of the walls more often each second, so the force on each unit of area is bigger.
(b) At A: 100 kPa × 60 cm³ = 6000 kPa cm³; at B: 300 kPa × 20 cm³ = 6000 kPa cm³, the same.
(c) V = 6000 kPa cm³ ÷ 150 kPa = 40 cm³.
(d) A straight line through the origin.
(e) A fixed mass of gas (none gets in or out) and a constant temperature.

Also accept

(a) more frequent hits on each cm²; (b) 6000 and 6000 kPa cm³; (c) 40 cm³; (d) straight line through the origin; (e) fixed mass, constant temperature

Watch for

“(a) At B the particles move faster.” — The temperature is constant, so the particles keep the same speed. They hit the walls more often because they have less space.
“(c) 150 kPa is half of 300 kPa, so the volume is half of 20 cm³: 10 cm³.” — A lower pressure goes with a bigger volume. Halving the pressure from B doubles the volume: 20 × 2 = 40 cm³, which is also 6000 ÷ 150.

2. GK2 · Final check

Model answer. (a) The pressure rises steadily, by 5 kPa for every 15 °C, from 100 kPa at 30 °C to 120 kPa at 90 °C. As the air warms its particles move faster, so they hit the walls more often and harder: the force on each unit of area of the walls rises. (b) T = 90 + 273 = 363 K. (c) At 60 °C the pressure is 110 kPa, only 10 kPa more than the 100 kPa at 30 °C, not double. Doubling a temperature in °C does not double the pressure, because 0 °C is not where the pressure is zero. (d) Each 15 °C colder takes 5 kPa off. 100 kPa ÷ 5 kPa = 20 steps of 15 °C, which is 300 °C below 30 °C: about −270 °C. In kelvin that is −270 + 273 = 3 K. These readings are rounded, so the true value is close to −273 °C, which is 0 K. (e) To change kelvin into °C, subtract 273: θ = 250 − 273 = −23 °C.

A full answer includes

(a) The pressure rises by the same 5 kPa for each 15 °C: warmer particles move faster and hit the walls more often and harder, so the force on each unit of area rises.
(b) 90 + 273 = 363 K.
(c) At 60 °C the pressure is 110 kPa, not 200 kPa: only 10 kPa more than at 30 °C.
(d) The pressure falls 5 kPa for each 15 °C colder, so 100 kPa is used up after 20 steps, 300 °C below 30 °C: about −270 °C. In kelvin, −270 + 273 = 3 K: close to −273 °C, which is 0 K.
(e) 250 − 273 = −23 °C.

Also accept

(a) steady rise of 5 kPa per 15 °C; faster particles, more often and harder hits; (b) 363 K; (c) 110 kPa, not 200 kPa; (d) about −270 °C, 3 K (close to −273 °C, 0 K); (e) −23 °C

Watch for

“(c) The pressure does double, because 60 °C is twice 30 °C.” — The table shows 110 kPa at 60 °C, not 200 kPa. The Celsius scale does not start where the pressure is zero.
“(d) The pressure would reach zero at 0 °C.” — Going down from 30 °C to 0 °C takes off only 10 kPa, so the pressure there is still about 90 kPa. Keep going.
“(e) 250 K is 523 °C.” — Going from kelvin to °C, subtract 273: 250 − 273 = −23 °C. A temperature in kelvin is always the bigger number.

3. GK3 · Final check

Model answer. (a) Steel expands when it warms and contracts when it cools, so the bridge is a little longer on a hot day than on a cold one. The expansion joints give it room to change length: the teeth slide between each other, so the bridge does not push against the road at its ends, bend or crack. (b) The particles of steel do not get bigger. Warming makes them vibrate more about their fixed positions, so they push each other slightly further apart and the bridge gets longer. (c) The air expands most; the iron expands least. (d) In iron, a solid, strong forces hold the particles close together in fixed positions; warming only makes them vibrate more. In ethanol, a liquid, the particles are close together but can move past each other and are held less tightly, so they spread further apart. In air, a gas, the particles are far apart and move fast with very weak forces between them, so nothing holds them together and they spread out most. (e) The free end moves down. The copper gets longer than the iron, so the strip curls with the copper on the outside of the curve. The copper is on top, so the top is the outside of the curve and the free end bends downwards.

A full answer includes

(a) The bridge expands on hot days and contracts on cold days; the joints give it room to change length without pushing on the road at its ends, bending or cracking.
(b) The particles stay the same size; they vibrate more about their fixed positions and end up slightly further apart.
(c) Air expands most; iron expands least.
(d) Iron: particles close together in fixed positions with strong forces, only vibrating more. Ethanol: close but able to move past each other, held less tightly. Air: particles far apart, moving fast, with very weak forces, so they spread out most.
(e) The free end bends down: the copper expands more, so it ends up on the outside of the curve, which is the top.

Also accept

(a) room to expand and contract; (b) same size, vibrate more, further apart; (c) air most, iron least; (d) forces and spacing; (e) down, copper on the outside of the curve

Watch for

“(e) The free end moves up, because the copper on top expands upwards.” — The copper gets longer, not taller. The strip curls with the longer copper on the outside of the curve, so with the copper on top the end bends down.
“(c) Iron expands most, because metals conduct heat well.” — How much something expands depends on the forces between its particles and how far apart they are. Iron, a solid, expands least.