Page 86 - Physics Coursebook 2015 (A level)

Cambridge International AS Level Physics
74
A gas doing work
Gases exert pressure on the walls of their container. If
a gas expands, the walls are pushed outwards – the gas has done work on its surroundings. In a steam engine, expanding steam pushes a piston to turn the engine, and in a car engine, the exploding mixture of fuel and air does the same thing, so this is an important situation.
piston pushed by gas
s
QUESTIONS
4 The crane shown in Figure 5.9 lifts its 500 N load to the top of the building from A to B. Distances are as shown on the diagram. Calculate how much work is done by the crane.
B
50 m
30 m
Figure 5.9 For Question 4. The dotted line shows the track of the load as it is lifted by the crane.
5 Figure 5.10 shows the forces acting on a box which is being pushed up a slope. Calculate the work done by each force if the box moves 0.50 m up the slope.
gas
A
40 m
Figure 5.8 When a gas expands, it does work on its surroundings.
Figure 5.8 shows a gas at pressure p inside a cylinder of cross-sectional area A. The cylinder is closed by a moveable piston. The gas pushes the piston a distance s. If we know the force F exerted by the gas on the piston, we can deduce an expression for the amount of work done by the gas. force
From the definition of pressure (pressure = area ), the force exerted by the gas on the piston is given by:
force = pressure × area
F=p×A
and the work done is force × displacement:
W = p×A×s
But the quantity A × s is the increase in volume of the gas; that is, the shaded volume in Figure 5.8. We call this ΔV, where the Δ indicates that it is a change in V. Hence the work done by the gas in expanding is:
W = pΔV
Notice that we are assuming that the pressure p does not change as the gas expands. This will be true if the gas is expanding against the pressure of the atmosphere, which changes only very slowly.
A
100 N
100 N
Figure 5.10 For Question 5.
6 When you blow up a balloon, the expanding balloon pushes aside the atmosphere. How much work is done against the atmosphere in blowing up a balloon to a volume of 2 litres (0.002 m3)? (Atmospheric pressure = 1.0 × 105 N m−2.)
70 N
30 N θ 45°