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 of the internal energy of the gas in the left - hand compartment to that of the gas in the right-hand compartment. (iv) Discuss whether it is correct to describe the final state of the system as an equilibrium state.

Page 6 of 15 9814(2024) H3 Physics Thermal Physics – Tutorials 3 (a) In the simple kinetic theory of an ideal gas, it is assumed that the gas contains a very large number of molecules, that they move at random, and that they make perfectly elastic collisions with the walls of the container. Explain why these assumptions are vital to the theory. (b) Use kinetic theory ideas to show that the number x of gas molecules striking an area A of the wall of the container in unit time is given by 1 6x nA c= where n is the number density of molecules in the container (the number per unit volume) and c is their average speed.

Page 7 of 15 9814(2024) H3 Physics Thermal Physics – Tutorials (c) Experiments on the properties of solid surfaces are often hampered by the presence of a layer of gas molecules sticking to the surface. To avoid this, the experiment may be carried out in a vacuum chamber in which the number density of gas molecules is relatively small. Such a chamber is maintained at a pressure of 5.0  10−8 Pa. The gas in the chamber is oxygen at 20 C. A scientist wants to do an experiment on the surface properties of a semiconductor crystal in the chamber. A clean surface of area 1.0  10−5 m2 can be generated by cutting the crystal, but when oxygen molecules strike the test surface they stick to it instead of rebounding elastically. When more than two oxygen molecules stick for every ten semiconductor atoms in the clean surface, the surface properties are significantly changed. (i) Estimate the number density of oxygen molecules in the chamber and their root mean square speed. Any kinetic theory equation required may be quoted without proof. [mass of oxygen molecule = 5.3  10−26 kg] (ii) From your knowledge of the approximate size of atoms, make an order -of- magnitude estimate of the number of semiconductor atoms in the uppermost layer of the clean test surface.

Page 8 of 15 9814(2024) H3 Physics Thermal Physics – Tutorials (iii) Estimate the time that the scientist has available to carry out the experiment before the test surface becomes significantly contaminated. Make use of your answers in (i) and (ii), and assume that the average speed is equal to the root- mean-square speed.

Page 9 of 15 9814(2024) H3 Physics Thermal Physics – Tutorials First Law of Thermodynamics 4 (a) (i) Write down an equation representing the First Law of Thermodynamics. Define the symbols you use. (ii) “The internal energy is determined by the state of the system.” Explain what this means, and discuss whether heating and work, like internal energy, are functions of state.

Page 10 of 15 9814(2024) H3 Physics Thermal Physics – Tutorials (b) A compressor takes in air at atmospheric pressure of 1.0  105 Pa and density 1.2 kg m−3. The compressed air is delivered at a pressure of 1.0  106 Pa and at a flow rate of 0.015 m 3 s−1. Assume that the compression takes place at constant temperature, and that air behaves as an ideal gas. (i) Find the work required to compress 1.0 kg of air in this compressor. (ii) Assuming that there are no frictional losses in the compressor, calculate the power needed to drive it.