Answers · Gas pressure and temperature

Gas pressure and temperature — return questions key

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

1. GR1 · Return

Model answer. (a) The particles of a gas move fast, at random, in all directions. When one hits a wall it bounces off and gives the wall a small push; billions of billions of hits each second add up to a steady force. (b) The pressure is the force of these hits on each unit of area of the wall. (c) In a smaller volume the same particles are more crowded. At a constant temperature they move at the same speed, but each square centimetre of the walls is hit more often each second, so the force on each unit of area, the pressure, rises. (d) p₁V₁ = p₂V₂: 100 kPa × 80 cm³ = 8000 kPa cm³ = p₂ × 50 cm³, so p₂ = 160 kPa. (e) p against V is a curve that falls steeply at small volumes and gets flatter at large ones; p against 1/V is a straight line through the origin.

A full answer includes

(a) The particles move fast at random; they hit the walls and bounce off, and each hit pushes on the wall.
(b) The pressure is the force of the hits on each unit of area of the wall.
(c) The same particles have less 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 rises.
(d) 100 kPa × 80 cm³ = p₂ × 50 cm³, so p₂ = 8000 ÷ 50 = 160 kPa.
(e) p against V: a curve that falls and gets flatter. p against 1/V: a straight line through the origin.

Also accept

(a) random hits on the walls; (b) force on each unit of area; (c) more frequent hits; (d) 160 kPa; (e) curve; straight line through the origin

Watch for

“(d) p₂ = 100 × 50 ÷ 80 = 62.5 kPa.” — Squeezing the gas into a smaller volume must raise its pressure. Keep p × V the same: 8000 ÷ 50.
“(c) The particles get smaller, so the pressure rises.” — The particles keep their size and, at a constant temperature, their speed. They hit the walls more often because they have less space.

2. GR2 · Return

Model answer. (a) Heating makes the particles move faster. With the volume fixed, faster particles reach the walls more often and hit them harder, so the force on each unit of area, the pressure, rises. (b) T (in K) = θ (in °C) + 273. (c) 100 °C = 373 K; 250 K = 250 − 273 = −23 °C. (d) At about −273 °C, which is 0 K. (e) The rise is 10 °C, which is 10 K, because a kelvin is the same size as a degree Celsius.

A full answer includes

(a) The particles move faster, so they hit the walls more often and harder: a bigger force on each unit of area.
(b) T (in K) = θ (in °C) + 273.
(c) 100 + 273 = 373 K; 250 − 273 = −23 °C.
(d) About −273 °C, which is 0 K.
(e) 10 K: a change of 1 °C is a change of 1 K.

Also accept

(a) faster, more often, harder; (b) T = θ + 273; (c) 373 K, −23 °C; (d) −273 °C, 0 K; (e) 10 K

Watch for

“(e) The rise is 10 + 273 = 283 K.” — Add 273 only to a temperature, not to a change in temperature. A rise of 10 °C is a rise of 10 K.
“(c) 250 K = 250 + 273 = 523 °C.” — From K to °C subtract 273. The number in °C is always the smaller one.

3. GR3 · Return

Model answer. (a) Solids, liquids and gases all expand when warmed and contract when they cool. Their particles do not grow; they move faster, or vibrate more, and spread further apart. (b) Gases expand most, then liquids, then solids. Gas particles are far apart with very weak forces between them, so they spread out a long way. Liquid particles are close together but can move past each other, so they spread out less. Solid particles are held in fixed positions by strong forces and only vibrate more, so solids expand least. (c) For example, liquid-in-glass thermometers, and bimetallic strips in thermostats and fire alarms. (d) For example, railway lines could buckle, so they have gaps or are welded and laid stretched; and bridges grow in summer, so they have expansion joints. (e) The brass gets longer than the steel, so the strip curls, with the brass on the outside of the curve.

A full answer includes

(a) All three expand when warmed and contract when cooled; the particles move faster or vibrate more and spread further apart, but do not get bigger.
(b) Gas most, liquid next, solid least: gas particles are far apart with very weak forces; liquid particles are close but can move past each other; solid particles are held in fixed positions by strong forces.
(c) Any two: liquid-in-glass thermometers; bimetallic strips in thermostats or fire alarms; loosening a metal lid on a glass jar with hot water.
(d) Any two, with the fix: rails (gaps, or welded rails laid stretched); bridges (expansion joints); power cables (hung with slack); full containers (leave space at the top).
(e) It curls, with the brass, which expands more, on the outside of the curve.

Also accept

(a) expand, contract; (b) gas, liquid, solid, with forces and spacing; (c) thermometer, thermostat; (d) gaps in rails, expansion joints; (e) curls with brass outside

Watch for

“(b) Solids expand most, because they are the hardest.” — Strong forces between the particles of a solid keep it from expanding much. Gases, with very weak forces, expand most.
“(e) The strip gets longer but stays straight.” — The two metals are joined, so one cannot slide past the other. The brass gets longer than the steel, so the strip must curl.