Question

Question 11 The following properties of titanium (Ti) are relevant to this question. Units Symbol Value Property 4.506 gcm-3 Density 47.9 g mol-I M Molar mass 8,6 x 10- K- 25.6 21.9 Coefficient of thermal expansion Molar heat capacity Thermal conductivity J mol- K- Wm- K- C k A titanium disc, which has a radius of exactly 10cm and thickness of exactly 5 mm at -20 °C, has a hole of radius exactly 1 cm drilled out of its centre. (a) (i) What is the volume of the disc? (ii) What is its mass? (iii) How many titanium atoms are there in the disc? [2 marks] (b) To what temperature must the disc be heated to increase its radius to 10.01 cm? [1 mark] (c) Describe how the size of the hole changes as the disc is heated and explain why [3 marks] The disc is heated to 90°C and then brought into contact with 50 g of water whose initial temperature is 10°C. The disc and water are heat capacity of water is cw 4.186 kJ kg K thermally isolated. The specific (d) What is the final equilibrium temperature of the disc and the water? [2 marks] The disc is then cooled to 0 °C and placed on a flat block of ice at the same temperature. There is perfect thermal contact at the interface. A large metal pot containing water which is at 20 °C is placed on the disc. Steady-state conduction is rapidly established. The latent heat of fusion of water is Lt 333 kJ kg1. (You may assume that the pot is very thin and that the water is well-stirred, so that all thermal effects other than conduction to the ice, like the cooling of the water or the pot, or horizontal loss of heat, can be ignored.) (e) At what initial steady rate (in units of grams per minute) does the ice begin to melt due to transfer of heat through the titanium from the water to the ice? [5 marks]

Answer 1

disc itanium the Volume The hickness 5 mm Tadius and to Cm 3 m 3 TK (01)xS x 0 The volume , of hole Ihe m 3. 1.53 X10 m3 Volume ef disc =(157 X10 - 1.57 m3 The na ss disr 4.50L X1o 0.69527 The mole nunoen 0.69523 14.515 nole. The atoms f numbers is 6.023 X(023 The of atom n 14.S1s numbes mole is 23 6.023 Xro 4.515 .2 3 mole cuder The (A new volume VoLIlt-to) ss330ss43rx 1 -4 1t 8.6x10 1o02 o t.tl-