(a) State the general gas equation for a fixed mass of an ideal gas and name the three gas laws from which it is derived. (4 marks) (b) A fixed mass of gas occupies $6$ litres at a pressure of $100$ kPa and a temperature of $300$ K. Find its volume when the pressure is raised to $200$ kPa and the temperature to $400$ K. (5 marks) (c) A steel rod is $2$ m long at $20\ ^\circ$C. Calculate its increase in length when heated to $70\ ^\circ$C. (Linear expansivity of steel $= 12 \times 10^{-6}$ K$^{-1}$.) (4 marks) (d) Give two practical consequences of thermal expansion that engineers must allow for. (2 marks)