NAME IB PHYSICS HL REVIEW PACKET: THERMODYNAMICS 1. This question is about gases and specific heat capacity. (a) State what is meant by an ideal gas.......... An ideal gas occupies a volume of 1.2 m 3 at a temperature of 27 C and a pressure of 1.0 10 5 Pa. The density of the gas is 1.6 kg m 3. It is found that 1.5 10 4 J of energy is required to raise the temperature of the gas to 52 C when the gas is held at constant volume. Determine the specific heat capacity at constant volume of the gas............. (3) A second sample of the same gas as above is heated from 27 C to 52 C at constant pressure. (i) Show that the volume of the gas at 52 C is 1.3 m 3....... Calculate the work done by the gas during the heating process....... (d) The specific heat capacity for the gas kept at constant volume is different to that when the gas is kept at constant pressure. State and explain whether the specific heat capacity for an ideal gas at constant pressure is greater or less than the specific heat capacity of the gas at constant volume............. (3) (Total 12 marks) 1
2. This question is about the change of phase (state) of ice. A quantity of crushed ice is removed from a freezer and placed in a calorimeter. Thermal energy is supplied to the ice at a constant rate. To ensure that all the ice is at the same temperature, it is continually stirred. The temperature of the contents of the calorimeter is recorded every 15 seconds. The graph below shows the variation with time t of the temperature θ of the contents of the calorimeter. (Uncertainties in the measured quantities are not shown.) 20 15 10 5 C 0 5 10 15 (a) 20 0 25 50 75 100 125 150 175 200 t / s On the graph above, mark with an X, the data point on the graph at which all the ice has just melted. Explain, with reference to the energy of the molecules, the constant temperature region of the graph................ (3) The mass of the ice is 0.25 kg and the specific heat capacity of water is 4200 Jkg 1 K 1. Use these data and data from the graph to (i) deduce that energy is supplied to the ice at the rate of about 530 W........... (3) 2
determine the specific heat capacity of ice......... (3) (iii) determine the specific latent heat of fusion of ice......... (d) State what property of the molecules of the ice is measured by a change in entropy.... (e) State, in terms of entropy change, the second law of thermodynamics....... (f) State what happens to the entropy of water as it freezes. Outline how this change in entropy is consistent with the second law of thermodynamics...................... (4) (Total 18 marks) 3
3. This question is about thermodynamic processes. (a) Distinguish between an isothermal process and an adiabatic process as applied to an ideal gas.......... An ideal gas is held in a container by a moveable piston and thermal energy is supplied to the gas such that it expands at a constant pressure of 1.2 10 5 Pa. thermal energy piston The initial volume of the container is 0.050 m 3 and after expansion the volume is 0.10 m 3. The total energy supplied to the gas during the process is 8.0 10 3 J. (i) State whether this process is either isothermal or adiabatic or neither... Determine the work done by the gas......... (iii) Hence calculate the change in internal energy of the gas......... (Total 6 marks) 4
4. Expansion of a gas An ideal gas at an initial pressure of 4.0 10 5 Pa is expanded isothermally from a volume of 3.0 m 3 to a volume of 5.0 m 3. (a) Calculate the final pressure of the gas....... On the axes below draw a sketch graph to show the variation with volume V of the pressure p during this expansion. 5 p / 10 Pa 6 4 2 0 0 2 4 6 / m 3 (3) Use the sketch graph in to (i) estimate the work done by the gas during this process; explain why less work would be done if the gas were to expand adiabatically from the same initial state to the same final volume. (Total 7 marks) 5
5. This question is about an ideal gas. (a) The pressure P of a fixed mass of an ideal gas is directly proportional to the kelvin temperature T of the gas. That is, P T. State (i) the relation between the pressure P and the volume V for a change at constant temperature; the relation between the volume V and kelvin temperature T for a change at a constant pressure. The ideal gas is held in a cylinder by a moveable piston. The pressure of the gas is P1, its volume is V1 and its kelvin temperature is T1. The pressure, volume and temperature are changed to P2, V2 and T2 respectively. The change is brought about as illustrated below. / P1, V 1, T1 P, V, T P2, V 2, T2 2 1 heated at constant volume to / pressure P and temperature T 2 heated at constant pressure to volume V 2 and temperature T 2 State the relation between (i) P1, P2, T1 and T. V1, V2, T and T2. Use your answers to to deduce, that for an ideal gas PV = KT where K is a constant............. (4) 6
6. This question is about an ideal gas. A sample of an ideal gas passes through the cycle of ABCA shown on the pressure/volume (p/v) diagram below. pressure / 10 Pa 5 14 12 10 C 8.0 6.0 4.0 2.0 A B 0.0 0.0 2.0 4.0 6.0 8.0 10 4 3 volume / 10 m The temperature of the gas at A, the starting point of the cycle, is 17 C. (a) (i) State which change, AB, BC or CA, is isochoric. Calculate the temperature of the gas at point B. (iii) Calculate the temperature of the gas at point C. During the change AB, 300 J of thermal energy is supplied to the gas. Determine the change in internal energy of the gas............. (3) During the change BC, 250 J of thermal energy is transferred. The area ABC on the pressure/volume diagram represents 120 J of energy. Calculate the thermal energy transfer during the stage CA. Explain your working.......... (3) (Total 11 marks) 7
7. This question is about entropy changes. (a) State what is meant by an increase in entropy of a system....... State, in terms of entropy, the second law of thermodynamics.......... When a chicken develops inside an egg, the entropy of the egg and its contents decreases. Explain how this observation is consistent with the second law of thermodynamics.......... (Total 5 marks) 8. This question is about a heat engine. A quantity of an ideal gas is used as the working substance of a heat engine. The cycle of operation of the engine is shown in the p-v diagram below. 5 p / 10 Pa 12.0 A B 8.0 4.0 C 0 0 2 4 6-3 3 V / 10 m The temperature of the gas at A is 300 K. (a) Calculate the temperature, at B, of the gas.......... 8
During the change A B the change in internal energy of the gas is 7.2 kj. Determine the amount of thermal energy transferred.......... State why, for the change B C, the change in the internal energy of the gas is numerically the same as that in....... (d) The work done on the gas in the change C A is 2.6 kj. Calculate (i) the net work done in one cycle..... the efficiency..... (Total 10 marks) 9. This question is about thermodynamic processes. (a) State what is meant by the concept of internal energy of an ideal gas....... The diagram below shows the variation with volume of the pressure of a fixed mass of an ideal gas. pressure B A C 0 0 volume 9
The change from B to C is an isothermal change at 546 K. At point A, the pressure of the gas is 1.01 10 5 Pa, the volume of the gas is 22.0 m 3 and the temperature of the gas is 273 K. (i) State the temperature of the gas at point C; Calculate the volume of the gas at point C. For the change from B to C, 31.5 10 5 J of thermal energy is transferred to the gas. (i) State the work done in the change from A to B. Determine the work done during the change C to A. (iii) Explain whether the work in is done by the gas or on the gas. (iv) Determine the work done by the gas during one cycle ABCA. (Total 11 marks) 10
10. This question is about mechanical power and heat engines. Mechanical power (a) Define power....... A car is travelling with constant speed v along a horizontal straight road. There is a total resistive force F acting on the car. Deduce that the power P to overcome the force F is P = Fv....... A car drives up a straight incline that is 4.80 km long. The total height of the incline is 0.30 km. 4.80 km 0.30 km The car moves up the incline at a steady speed of 16 m s 1. During the climb, the average resistive force acting on the car is 5.0 10 2 N. The total weight of the car and the driver is 1.2 10 4 N. (i) Determine the time it takes the car to travel from the bottom to the top of the incline. Determine the work done against the gravitational force in travelling from the bottom to the top of the incline. (iii) Using your answers to (i) and, calculate a value for the minimum power output of the car engine needed to move the car from the bottom to the top of the incline. 11 (4)
(d) From the top of the incline, the road continues downwards in a straight-line. At the point where the incline starts to go downwards, the driver of the car in stops the car to look at the view. In continuing his journey, the driver decides to save fuel. He switches off the engine and allows the car to move freely down the incline. The car descends a height of 0.30 km in a distance of 6.40 km before levelling out. 0.30 km 6.40 km The average resistive force acting on the car is 5.0 10 2 N. Estimate (i) the acceleration of the car down the incline; (5) the speed of the car at the bottom of the incline. (e) In fact, for the last few hundred metres of its journey down the incline, the car travels at constant speed. State the value of the frictional force acting on the car whilst it is moving at constant speed.... 12
The heat engine (f) The diagram below shows the idealised pressure-volume (P-V) diagram for one cycle of the gases in an engine similar to that used in the car. pressure P B C D A volume V The changes A B and C D are adiabatic changes. (i) Explain what is meant by an adiabatic change. State the name given to the change B C. (g) The useful power output of the engine is 20 kw and the overall efficiency of the engine is 32. The car engine completes 50 cycles every second. Deduce that QH = 1.3 kj................ (3) (Total 24 marks) 13
1. (a) obeys the universal gas law / equation MARK SCHEME! pv T or molecules are elastic spheres of negligible volume; at all values of pressure, volume and temperature or no mutual force of attraction / repulsion; 2 mass of gas 1.6 1.2 = 1.9 kg; use of Q = mc ; 1.5 10 4 = 1.92 c (52 27) c = 310 J kg 1 K 1 ; 3 Award [1] for use of density in place of mass to give 375 J kg 1 K 1 and [0] for use of volume in place of mass. (i) use of V = 1.2 pv = constant; T 325 ; 300 = 1.3 m 3 2 max (d) use of W = p V; W = 1.0 10 5 0.1 = 1.0 10 4 J ; 2 thermal energy required to raise temperature (same as for constant volume); and to do work against the atmosphere; so must be larger; 3 Award [0] for a bald statement of answer or fallacious argument. 2. (a) (165, 0); 1 [12] Look for these points: to change phase, the separation of the molecules must increase; Some recognition that the ice is changing phase is needed. so all the energy input goes to increasing the PE of the molecules; Accept something like breaking the molecular bonds. KE of the molecules remains constant, hence temperature remains constant; 3 If KE mentioned but not temperature then assume they know that temperature is a measure of KE. (i) time for water to go from 0 to 15 C = 30 s; energy required = ms = 0.25 15 4 200 = 15 750 J; power = energy = 525 W 530 W; 3 time ice takes 15 s to go from 15 C to 0; energy supplied = 15 530 J; sp ht = (530 15) (15 0.25) = 2100 J kg 1 K 1 ; 3 (iii) time to melt ice =150 s; L = ( 150 530) 0.25 = 320 kj kg 1 ; 2 (d) the degree of disorder / order (of the molecules of the ice); 1 (e) in any process, (reaction, event etc) the overall entropy of the universe / a closed system increases ; 1 14
2. (Cont d) (f) entropy decreases; Award [1] each for any of these main points, up to [3 max]. when water freezes it gives out energy (heat); therefore speed (KE) of surrounding air molecules increases; the air surrounding the ice is therefore in a more disordered state; therefore disorder (entropy) of the universe increases; 4 max [18] 3. (a) isothermal: takes place at constant temperature; adiabatic: no energy exchange between gas and surroundings; 2 (i) neither; 1 W = P V = 1.2 10 5 0.05 = 6.0 10 3 J; 1 (iii) recognize to use Q = U + W; to give U = 2.0 10 3 J; 2 [6] 4. Expansion of a gas (a) 2.4 10 5 Pa; 1 any line through (3.0, 4.0) and (5.0, 2.4); that is a smooth curve in correct direction; that starts and ends on the above points; 3 (i) work done = area under line / curve / graph; to get 6.1 10 5 J; 2 Accept 5.5 6.7 10 5 J. work done would be less as adiabatic line is steeper than isothermal line / OWTTE; or: no energy / heat has to be transferred to the surroundings to maintain constant temperature / OWTTE; 1 [7] 15
5. (a) (i) P 1 or V V 1 P or PV = constant or pressure inversely proportional to volume, etc; 1 V T, etc; 1 (i) P1 T 1 P T 2 V V T or P1 T P2 T1 ; 1 1 2 or V 1T2 V2T ; 1 T2 P T T P 2 1 from (i) ; 1 2 from ; 1 V T T V 1 1 2 2 equate to get ; T1 T2 so that PV T 2 PV P V constant or PV = KT; 4 [8] 6. (a) (i) CA; 1 V T and T = 290K; temperature = 3 290 = 870 K; 2 Award [0] for 51C. (iii) p T; 12.5 temperature = 290 = 1800K; 2 2 102C scores [1] out of [2]. external work done = p V; = 2.0 10 5 6.0 10 4 = 120 J; change in internal energy (= 300 120) = 180J; 3 energy supplied to gas (= A B + B C) = 550J; work done going through cycle = 120 J / representing the area under the pressure volume graph; transfer in stage C A (= 550 120) = 430J; 3 [11] 16
7. (a) increase in the degree of disorder (in the system); 1 total entropy (of the universe); is increasing; 2 entropy of surroundings increases by a greater factor; because process gives off thermal energy / other appropriate statement; 2 V1 V2 8. (a) use of ; T1 T2 V2 6 T 2 T1 300 = 900 K; 2 V 2 1 [5] W(= p V = 12 10 5 4.0 10 3 = 4.8 10 3 J) = 4.8 kj; Q = (4.8 kj + 7.2 kj) = 12 kj; 2 Award full marks for correct answer without work shown. the (magnitude of the) temperature change is the same; the gas is ideal and so the change in internal energy depends only on temperature; 2 (d) (i) for the full cycle U = 0; therefore the net work is 4.8 2.6 = 2.2 kj; or net thermal energy in is 12 kj and net thermal energy out is 7.2 + 2.6 = 9.8 kj; so work done is 12 9.8 = 2.2 kj; or work is area in loop; area = 4.8 2.6 = 2.2 kj; 2 efficiency is 2.2 12 ; = 0.18 /18 %; 2 9. (a) internal energy: (random translational) kinetic energy of atoms / molecules; 1 [10] (i) 546 K; 1 temperature doubled but pressure remains constant; hence volume doubled to 44.0m 3 ; or V T; therefore, volume doubled to 44.0m 3 ; 2 (i) W = 0; 1 W = p A (V C V A ) = 1.01 10 5 22.0; = 22.2 10 5 J; 2 Note the ecf from. (iii) (iv) work done on the gas; because the volume is decreasing; 2 Award [0] for a bald statement without any attempt at reasoning. total work done by gas in cycle is W = 0 + 31.5 10 5 22.2 10 5 ; work output = 9.3 10 5 J; 2 [11] 17
10. (a) the rate of working / work time; 1 If equation is given, then symbols must be defined. P W t F d t ; v d therefore, P = Fv; 2 t d v (i) t ; 4800 300s; 16 2 W = mgh = 1.2 10 4 300 = 3.6 10 6 J; 1 (iii) work done against friction = 4.8 10 3 5.0 10 2 ; total work done = 2.4 10 6 + 3.6 10 6 ; total work done = P t = 6.0 10 6 ; 6 6 10 to give P 20kW; 4 0.30 6.4 300 (d) (i) sinθ 0.047; weight down the plane = W sin = 1.2 10 4 0.047 = 5.6 10 2 N; net force on car F = 5.6 10 2 5.0 10 2 = 60N; a F m ; 60 2 2 5.0 10 ms ; 3 1.2 10 5 v 2 = 2as = 2 5 10 2 6.4 10 3 ; to give v = 25 / 26ms 1 ; 2 Give full credit for (i) and to candidates who use energy argument to calculate v and then use this to calculate a. gain in KE = loss in PE work done against friction; 1 2 2 mv mgh Fd ; 1 2 6 2 2 mv 3.6 10 5.0 10 6.40; 0.6 10 3 v 2 = 3.6 10 6 5.0 10 2 6.40; v = 25 / 26ms 1 ; 2 a v ; 2s = 5.0 / 5.1 10 2 ms 2 ; (e) 5.6 10 2 N; 1 (f) (i) a compression or expansion / change in state (of the gas); in which no (thermal) energy is exchanged between the gas and the surroundings / in which the work done is equal to the change in internal energy of the gas; 2 isobaric; 1 18
10. (Cont d) 20 (g) (for real engine) 0. 32 P H to give PH = 63kW; time for one cycle = 0.02s; QH = PH time to give QH = 6.3 10 4 0.02; = 1.3kJ or eff W Q H ; 2 10 W 50 0.32 400 4 400J; to give QH = 1.3 kj; 3 QH [24] 19