P1V1 = P2V2 = constant
P = pressure
V = volume
P1 / T1 = P2 / T2 = constant
P = pressure
T = temperature in Kelvin
A diver works in the sea on a day when the atmospheric pressure is 101 kPa. The diver uses compressed air to breathe under water. 1700 litres of air from the atmosphere is compressed into a 12-litre gas cylinder. The compressed air quickly cools to its original temperature. Calculate the pressure of the air in the cylinder.
P1V1 = P2V2
101 x 1700 = P2 x 12
pressure of air in the cylinder = 101 x 1700 / 12 = 14000 kPa
The gas in a cylinder has a pressure of 210kPa at a temperature of 27°C. Calculate the new pressure when the temperature of the gas rises to 81°C.
27°C = (27+273)K = 300K
81°C = (81+273)K = 354K
P1 / T1 = P2 / T2
210 / 300 = P2 / 354
P = 210 x 354 / 300 = 247.8 kPa
A student blows up two balloons to the same size.She puts one balloon into a freezer. After a while, the student compares the two balloons. The balloon that has been cooled is smaller.
(a) Use ideas about particles to explain why the cooled balloon is smaller.
- At lower temperature, particles have lower kinetic energy and move at lower speed
- The particles hit the balloon less often with a lower speed.
- Change in momentum of the particles is reduced, so force on the walls of the balloon is reduced, which reduces the pressure on the balloon.
- With smaller pressure from inside the balloon, the cooled balloon becomes smaller in size.
- To have a better control the temperature of the balloon, instead of putting the balloon into the freezer for different times, put the balloon into different freezers set at different temperature.
- It is difficult to measure the temperature of the balloon using a thermometer; measure the temperature of the freezer instead.
- Measuring size of the balloon is not a precise measure; choose a more precise measure of the size, such as diameter of the balloon.
- It is difficult to measure the size of the balloon by lining the balloon up next to a ruler; wrap a string around the center of the balloon to measure the diameter of the balloon.
- Since the balloon may warm up while it is waiting to be measured after taken out of the freezer, do the measurements as quickly as possible.
- Repeating the experiment three times is not making sure it is a fair test; to make sure it is a fair test, a controlled variable should remain constant for all experiments, such as the initial diameter of the balloon before putting it in a freezer.