Question

. A quantity of gas is trapped by a piston in a cylinder with thin metal walls. The piston is free to move without friction within the cylinder. a) The air in the freezer is at atmospheric pressure, which is 1.0 × 105Pa. The area of the piston in contact with the air in the freezer is 2.4 × 10–3m2 .

i. Calculate the force exerted on the piston by the air in the freezer.
ii. When the cylinder is first placed into the freezer, the temperature of the gas in the cylinder decreases
and the air pushes the piston into the cylinder. Calculate the work done on the piston by the air in the
freezer as the air pushes the piston at distance of 0.021m into the cylinder.
b) The initial temperature of the cylinder and the gas is 21°C and, in the freezer, the temperature of the
cylinder decreases to –18°C. The thermal capacity of the cylinder is 89J/ °C. Calculate the change in
the internal energy of the cylinder.

Answer 1

i) To find the force exerted on the piston by the air.

We use the force formula: F = mass x acceleration.

Except, we use pressure and area.

So our new formula will be:

Force = Pressure x Area

Now we simply input the pressure and area values, from the question.

Our equation that we need to solve:

Force = 1.0 x 10^5 x 2.4 x 10^-3

= 240N

ii) To calculate the work done on the piston by the air.

The formula we need to use here:

W= f x d

Or: Work Done = Force x Distance.

Using our force from the previous question, we just need to substitute the values into the formula again. Gaining the distance from the question. Since the distance is already in meters (m) we don't need to convert any units.

Work Done = 240 x 0.021

5.04J

b) To calculate change in internal energy change.

The formula here is ΔU = Q + W., however we can simplify this down to make this easier.

Change in internal energy = Heat exchanged x Work Done

We already found the work done, and we can calculate heat exchanged by finding the temperature difference which is:

39°C

ΔU = 39 + 5.04

44.04