Distinguish between an isothermal process and an adiabatic process as applied to an ideal gas (2)
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1 1. 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 Pa. thermal energy piston The initial volume of the container is m 3 and after expansion the volume is 0.10 m 3. The total energy supplied to the gas during the process is J. (b) (i) State whether this process is either isothermal or adiabatic or neither... (ii) Determine the work done by the gas
2 (iii) Hence calculate the change in internal energy of the gas (Total 6 marks) 2. This question is about ideal gases and specific heat capacity. (a) (i) State, in terms of kinetic theory, what is meant by an ideal gas (ii) Explain why the internal energy of an ideal gas is kinetic energy only A fixed mass of an ideal gas has a volume of 870 cm 3 at a pressure of Pa and a temperature of 20.0 C. The gas is heated at constant pressure to a temperature of 21.0 C. (b) (i) Calculate the change in volume of the gas
3 (ii) Determine the external work done during this process (c) (i) Define specific heat capacity (ii) Explain what happens to the molecules of an ideal gas when the temperature of the gas is increased at constant volume (iii) Apply the first law of thermodynamics to show that, if the temperature of a gas is raised at constant pressure, the specific heat capacity of the gas is different from that when the temperature is raised at constant volume (Total 17 marks) 3
4 3. Expansion of a gas An ideal gas at an initial pressure of 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 (b) 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 / m 3 (c) Use the sketch graph in (b) to (i) estimate the work done by the gas during this process; 4
5 (ii) 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
6 4. Thermodynamics The graph below shows the variation with volume V of the pressure p for two isothermal changes of two ideal gases X and Y. The gases have the same number of moles. The dots indicate two particular states of the gases, (p X, V X ) and (p Y, V Y ). p X Y p X p Y 0 0 V V X Y V (a) State what is meant by an isothermal change
7 (b) Explain whether gas X in the state (p X, V X ) is at a higher or lower temperature than gas Y in the state (p Y, V Y ) (c) Gas Y is compressed adiabatically from state (p Y, V Y ) until it reaches the pressure p X. (i) Explain whether the temperature of gas Y will increase, decrease or stay the same during this process. (ii) On the graph opposite, draw a line to represent this adiabatic compression of gas Y. (d) On the graph opposite, shade the area that represents the work done when gas X is compressed isothermally from volume V Y to volume V X. (Total 11 marks) 5. This question is about entropy changes. (a) State what is meant by an increase in entropy of a system
8 (b) State, in terms of entropy, the second law of thermodynamics (c) 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
9 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 C A B 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. (ii) Calculate the temperature of the gas at point B. (iii) Calculate the temperature of the gas at point C. 9
10 (b) During the change AB, 300 J of thermal energy is supplied to the gas. Determine the change in internal energy of the gas (c) 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 (Total 11 marks) 10
11 7. This question is about thermodynamic processes. (a) On the diagram below, draw arrows to show the energy transfers associated with a heat pump. hot resevoir cold resevoir 11
12 (b) The diagram below, shows the relation between the pressure P and the volume V of the working substance of the heat pump for one cycle of its operation. P B A C D V (i) The working substance at point C of the cycle is in the liquid phase. State the reason why both the changes from C D and A B are isothermal isobaric changes. C D A B (ii) State during which process of the cycle energy is absorbed from the cold reservoir and during which process energy is transferred to the hot reservoir. Energy absorbed from cold reservoir Energy transferred to hot reservoir (iii) State how the value of the work done during one cycle may be determined from the PV diagram. (Total 8 marks) 12
13 8. This question is about the first law of thermodynamics and about a steam engine. (a) State the first law of thermodynamics (b) An ideal gas in a cylinder is compressed by a piston. ideal gas The work done on the gas is 250 J and the change in internal energy of the gas is 150 J. Explain how these energy changes are consistent with the first law of thermodynamics
14 (c) In one cycle of a steam engine, water is heated at high pressure until changed into steam at a very high temperature. This steam expands and is then compressed such that it turns back to water. The graph below shows the idealised relationship between the pressure P and volume V of the water and steam for one cycle of this steam engine. P / 10 5 Pa V / 10 m 3 (i) Use the graph above to deduce that the work done by the engine in one cycle is approximately J. 14
15 (ii) As a result of compressing the steam, the energy transferred to the surroundings is approximately J. Estimate the efficiency of the steam engine. (Total 10 marks) 9. This question is about temperature, internal energy and thermodynamics. (a) Two solid objects undergo the same temperature change. A student states that the change in internal energy of the two objects would be the same. Briefly discuss this statement
16 (b) (i) State, in terms of entropy change, the second law of thermodynamics. (ii) When an ice crystal forms from liquid water, the entropy of the water decreases. By reference to the second law, discuss the entropy change. (c) The diagram below shows the relation between the pressure P and the volume V of an ideal gas for one cycle ABCDA of a Carnot cycle. P A B D C V For the change from B to C, (i) state the name of this change; 16
17 (ii) discuss, by reference to the first law of thermodynamics, the transfers of energy. (Total 11 marks) 10. This question is about thermodynamic processes. (a) State what is meant by an adiabatic change (b) The diagram below shows the pressure-volume (p-v) changes for one cycle of the working substance of a refrigerator. 5 p / 10 Pa V / 10 m 17
18 On the diagram above, (i) (ii) (iii) draw arrows to show the direction of the changes; label with the letter A an isobaric change; label with the letter B the change during which thermal energy is transferred to the working substance. (c) Use data from the diagram in (b) to estimate the work done during one cycle of the working substance (d) (i) By referance to entropy change, state the second law of thermodynamics. 18
19 (ii) The cycle of the working substance in (b) reduces the temperature inside the refrigerator. Explain how your statement in (d)(i) is consistent with the operation of a refrigerator. (Total 11 marks) 11. This question is about p V diagrams. The graph below shows the variation with volume of the pressure of a fixed mass of gas when it is compressed adiabatically and also when the same sample of gas is compressed isothermally. 7.0 C pressure / x 10 Pa B volume / x 10 m 3 3 A
20 (a) State and explain which line AB or AC represents the isothermal compression (b) On the graph, shade the area that represents the difference in work done in the adiabatic change and in the isothermal change. (c) Determine the difference in work done, as identified in (b) (d) Use the first law of thermodynamics to explain the change in temperature during the adiabatic compression (Total 9 marks) 20
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