Solution: Option C
Solution: Option C
When temperature is constant (for o-level), when a fixed mass of gas (fixed number of air molecules) is compressed in a closed system (e.g. piston), the volume V decreases and pressure P increases, and vice versa.
But when you multiply pressure and volume, PV, it is always a constant.
PV = constant
Hence we can always equate the PV of the first scenario = to the PV of the second scenario, provided there is no addition or removal of air molecules from the system.
Hence, you have P1V1 = P2V2
The followings are 4 different questions which require this concept to solve. Do revise them.
Solutions: Option D (refer to the worked solutions below)
Solutions: Option D
Solution: Option C
The 3 states of matter – solid, liquid and gas.
In general, when a body is heated, it expands and volume increases. The mass remains the same. Since density = mass/volume, its density decreases (less dense). For instance, warm air rises as it is less dense. In terms of kinetic theory, the particles will increase in kinetic energy. The average spacing between the particles increases (assuming not in a closed container).
Likewise, when a body is cooled, the opposite occurs. The body contracts and volume decreases. It becomes denser.
Due to the differences in particles arrangement of solid, liquid and gas, each expands by different amount when heated and vice versa. Which expands the most when heated and contracts the most when cooled?
The following demonstration of the ‘Pee Boy’ is a good video to show the concepts.
The tiny hole at the penis is too small for any water to enter on its own. So using thermal transfer in the different states, the following steps are taken:
(a) (i) A bigger force than F can be obtained due to the level system and hydraulic system.
Level system: Applying principle of moments, the anticlockwise moment by the F is equal to the clockwise moment by the force on piston A (note that the handle is pushing the piston down, but the piston A is pushing on the handle upwards – action = reaction). As the perpendicular distance from F to the pivot is greater than the perpendicular distance of the force by piston to the pivot, the force on the piston A is greater than F at handle.
Hydraulic system: As the pressure transmitted in the liquid is the same, pressure at piston A = pressure at piston B. As P = F/A and area of piston A is smaller than area of piston B, a larger force is obtained in piston B.
Hence these two systems allow the force on piston B to be greater than F at the handle.
(a) (ii) Both liquid and gas molecules are in a continuously random motion. But in liquid, the molecules are closely packed together and able to slide around one another. There is very little empty space between the molecules hence liquid is not compressible. Gas molecules are far apart from one another, hence gas can be easily compressed.
(b) P = F/A = 12000 / 0.060 = 200 000 Pa
(c) Velocity is the vector quantity while speed is a scalar. As the car goes round the bend, the direction of the car changes. Hence velocity is changing even though speed is constant.
Likewise, as the velocity is changing, the car is considered to have an acceleration (not in the sense of increasing speed though).
PAVA = PBVB
(Patm + Pwater) VA = (Patm) VB
(10 + 20) VA = 10 x 6
VA = 60 / 30
= 2 cm3
Pressure of a fixed mass of gas, P, is inversely proportional to the volume of the gas, V, when the temperature is held constant.
P inversely proportional to V
P = k/V , where k is a constant.
PV = k
With these concepts, you should be able to sketch the various graph. Do not memorise them. Use your concepts from Maths to help you to recall instead.