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5 Thermodynamics 1 a) A fixed mass of an ideal gas is heated while its volume is kept constant. i. Sketch a graph to show how the pressure of the gas varies with temperature of the gas. ii. Now volume is fixed to a higher value, on the same axes sketch the P-T variation and label it A. b) A car tyre has a volume of 17200 cm3. At a temperature of 304 K the absolute pressure in the tyre is 228 kPa. How many moles of air must be pumped into the tyre to increase its pressure to 271 kPa, given that the temperature and volume of the tyre remain constant? The molar gas constant, R = 8.314 J K-1 mol-1 c) A cylinder of fixed volume 0.078 m3 contains 18 mol of an ideal gas at a pressure of 620 kPa. Calculate the average kinetic energy of a gas molecule in the cylinder. The molar gas constant, R = 8.314 J K-1 mol-?, Boltzmann's constant, k = 1.381 x 10-23 m2 kg s-2 K-1