Q. 15 (based on material in Units 16 and 18)
(a) During a flight, the air pressure in the cabin of a commercial aeroplane is maintained at 8.00 x 104 Pa using a system of gas cylinders and automatic valves. Note that 0K = 273.15 °C.
(i) The pilot decides to change the temperature of the cabin from 21.0°C to 23.0 °C. Assuming the pressure control system works perfectly, calculate the resultant change in the number density of air molecules in the cabin.
(ii) While the aeroplane is descending to land, the temperature of an aluminium plate on its hull rises from -25.0°C to 0.0°C. Due to the
change in temperature, the volume of the plate increases by
AV/V = 6.0 x 10-4. Calculate the volumetric expansivity coefficient of aluminium in this temperature range.
(b) Consider an enclosed ideal monatomic gas. The initial volume and pressure of the gas are VA and PA. The amount of gas is 1 mole.
Assume that any changes in the volume of the gas are frictionless.
(i) Draw axes of pressure (P) against volume (V). The enclosed gas is isothermally compressed to (VB, PB). Sketch the path followed by the gas while undergoing this change on your PV graph and label it
change 1.
(ii) Deduce an expression for the resultant change in entropy of the enclosed gas in terms of VA, VB, PA, PB, and the molar gas constant R.
(Hint: It is not necessary to derive an expression from first principles).
(iii) The gas is then adiabatically compressed to (Vc, Pc). Sketch the path followed by the gas while undergoing this change on your PV
graph and label it change 2.
(iv) State if the following are positive, negative, or zero for change 1 and for change 2:
-heat transfer to the enclosed gas,
- heat transfer to the environment.