(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
