(a) (i) Define relative density.
(ii) List three characteristics of pressure in a liquid.
(b) The horizontal door of a submarine at a depth of 500m has an area of 0.4m(^{2}). Calculate the force exerted by the sea water on the door at this depth. [Relative density of sea water = 1.03 ] [Atmospheric pressure =- 1.01 x 10(^{5}) Nm(^{-2})] [Density of pure water = 1000kgm(^{-3})] [g = 10ms(^{-2})]
(c) (i) List three effects of heat other than expansion.
(ii) Explain saturated vapour pressure.
(iii) A heating coil of resistance 20 (Omega) connected to a 220 V source is used to boil a certain quantity of water in a container of heat capacity 100 J kg(^{-1}) for 2 minutes. If the initial temperature of the water is 40° C, calculate the mass of the water in the container. [specific heat capacity of water = 4.2 x 10(^3) Jkg(^{-1}) K(^{-1})] [assume boiling point of water = 100°C]
Explanation
(a)(i) Relative density is the ratio of the density of the substance to the density of water
(ii) Characteristics of pressure in liquid are:
-pressure increases in direct proportion to the depth of the liquid -pressure at any point in a liquid acts equally in all directions
-pressure at all points at the same level within a liquid is the same
-pressure applied to an enclosed liquid is transmitted equally throughout the fluid.
(b) Force on the door F = Ah g = 0.4 x 500 x 1.03 x 103x 10 = 2.06x 106N
(c)(i) Effects of heat other than expansion are:
-Rise in temperature -Change of state
-Change of colour
-Change of electrical resistance
(ii) When a liquid and its vapour are in dynamic equilibrium, the vapour is said to be saturated. The pressure or force exerted on unit area of the container of such a saturated vapour is known as saturated vapour pressure.
(iii) Heat generated by coil = heat gained by water + container.
(frac{V^2t}{R}) = mc(theta_{text{water}}) + Q(_c theta_{text{container}})
(frac{220^2 times 2 times 2 times 60}{20}) = m x 4.2 x 10(^{3}) x 60 + 100 x 60
290400 = 252000m + 6000
m = (frac{290400 – 6000}{252000}) = 1.13kg