NYJC_EJC Thermal Physics Tutorial

Page 1 of 15 9814(2024) H3 Physics Thermal Physics – Tutorials H3 Thermal Physics Temperature 1 The measurement of temperature on the thermodynamic (kelvin) scale may be made using a special type of thermometer called a constant -volume gas thermometer. (To answer this data analysis question, you do not need to know anything about the working of this thermometer.) The pressure pT of a fixed mass of gas at constant volume is compared with the pressure ptr at a reference temperature (the triple point of water). The thermodynamic temperature T is given by T 0 tr 273.16 limit , → =  trp pT p where the notation T 0 tr 'limit ' →   trp p p means ‘the value of T tr p p for a vanishingly small value of ptr’. A constant volume gas thermometer is used to measure the thermodynamic temperature T of a bath containing a boiling liquid. The following readings are taken. T /kPap 17.64 55.00 74.42 93.59 /kPatrp 13.72 42.83 58.00 73.01 /T trpp (a) Calculate, to an appropriate number of significant figures, the corresponding values of T tr p p . Fill up the blanks in the table above. (b) Use a graphical method to obtain T 0 tr limit trp p p→    . 1.288 1.286 1.284 1.282 1.280 0 20 40 60 80 100 ptr / Pa T tr p p

Page 2 of 15 9814(2024) H3 Physics Thermal Physics – Tutorials (c) Hence calculate the thermodynamic temperature T of the boiling liquid. (d) Suggest why the value of T does not depend on the gas used in the thermometer.

Page 3 of 15 9814(2024) H3 Physics Thermal Physics – Tutorials Ideal Gas 2 (a) What do you understand by an ideal gas? The gas constant R in your data sheet is sometimes called the universal gas constant, because its value is the same for all gases (when they are treated as ideal). Use this fact to show that equal volumes of different ideal gases, under the same conditions of temperature and pressure, contain equal numbers of molecules. (b) Fig. 2.1 shows a closed cylinder 1.00 m long, which contains an ideal gas on each side of a freely-moving but gas-tight piston. The piston is a perfect thermal insulator. Fig. 2.1 Initially the gas on both sides of the piston is 27 C. The equilibrium position of the piston is then 0.40 m from the left-hand end of the cylinder, as shown in Fig. 2.1.

Page 4 of 15 9814(2024) H3 Physics Thermal Physics – Tutorials (i) For this initial state, find the ratio of the internal energy of the gas in the left - hand compartment to the internal energy of the gas in the right -hand compartment. The gas in the left-hand compartment is then heated very slowly to 177 C, the gas in the right-hand compartment being maintained at 27 C. (ii) Describe the motion of the piston. How far is its new equilibrium position from the original?

Page 5 of 15 9814(2024) H3 Physics Thermal Physics – Tutorials (iii) For this final state, find the ratio