H209 First Law of Thermodynamics 2.0 Tutorial (1718)

1 Topic 9: First Law of Thermodynamics Page 1 9749 H2 Physics Tutorial First Law of Thermodynamics Multiple Choice Questions 1. A fixed mass of gas undergoes changes of pressure and volume as shown in Fig. 1. When the gas is taken from state P to state R by the stages PQ and QR, 8J of heat are absorbed by it and 3J of work are done by it. When the same resultant change is achieved by stages PS and SR, 1J of work is done by the gas. In this case, A 12 J of heat are rejected. B 10 J of heat are absorbed. C 8 J of heat are absorbed. D 6 J of heat are absorbed. E 4 J of heat are rejected. (D) J83/II/29; N79/II/31 2. A sample of an ideal gas initially having internal energy U1 is allowed to expand adiabatically performing external work W. Heat Q is then supplied to it, keeping the volume constant as its new value, until the pressure rises to its original value. The internal energy is then U2. (See Fig. 2) The increase in internal energy U2 – U1 is equal to A zero B W C Q D Q - W E W - Q (D) N81/II/27 Fig.1 Fig.2

2 Topic 9: First Law of Thermodynamics Page 2 9749 H2 Physics Tutorial 3. A fixed mass of an ideal gas slowly absorbs 1000 J of heat and as a result expands slowly, at a constant pressure of 2.0 x 104 Pa, from a volume of 0.050m3 to a volume of 0.075m3. What is the effect on the internal energy of the gas? A It decreases by 1000 J. B It decreases by 500 J. C It is unchanged. D It increases by 500 J. E It increases by 1000 J. (D) N90/I/24; J86/I/25 4. A mass of an ideal gas of volume V at pressure p undergoes the cycle of changes shown in the graph. At which points is the gas coolest and hottest? coolest hottest A X Y B Y X C Y Z D Z X E Z Y 5. An ideal gas is taken through the three processes (A  B, B  C, and C  A) shown in the drawing. u is the increase in internal energy, Q is the heat supplied to the gas and W is the work done on the gas. Which of following shows the correct missing entries in the above table? A (b) 500 J (a) 0 B (c) 1436 J (e) -1124 J C (d) -4864 J (b) -561 J D (d) 4303 J (e) 1124 J 0 1 5 1 4 p/ 105 Pa V/ 10-10m3 Z Y X

3 Topic 9: First Law of Thermodynamics Page 3 9749 H2 Physics Tutorial Self-Attempt 6. An ideal gas undergoes an expansion in volume from 1.3 x 10-4 m3 to 3.6 x 10-4 m3 at a constant pressure of 1.3 x 105 Pa. During this expansion, 24 J of heat is supplied to the gas. What is the overall change in the internal energy of the gas? [-6 J] 7. A gas in a cylinder expands from a volume of 0.110 m3 to 0.320 m3. Heat flows into the gas just rapidly enough to keep the pressure constant at 1.80 x 10 5 Pa during the expansion. The total heat added is 1.15 x 105 J. (a) Find the work done by the gas. [3.78 x 104 J] (b) Find the change in internal energy of the gas. [7.72 x 104 J] 8. When water is boiled under a pressure of 2.00 atm, the heat of vaporization is 2.20 MJ kg-1 and the boiling point is 120 oC. At this pressure and temperature, 1.00 kg of water has a volume of 1.00 x 10-3 m3, and 1.00 kg of steam has a volume of 0.824 m3. [1 atm = 1.013 x 105 Pa] (a) Compute the work done when 1.00 kg of steam is formed at this temperature. (b) Compute the increase in internal energy of the water. (c) The work done for 1.00 kg of steam to form at 100 oC and 1 atm is 1.69 x 10 5 J, suggest a reason why the work done against external pressure decreases when external pressure increases. [1.66 x 105 J, 2.03 x 106 J] 9. During an adiabatic expansion, the temperature of 0.450 mol of argon (Ar) drops from 50.0 oC to 10.0 oC. Argon is monatomic and may be treated as an ideal gas. (a) What is the change in internal energy of the gas? (b) How much work does the gas do? Discussion questions 10. The cylinder in the figure shown below holds a volume V 1= 1.00 x 10-3 m3 of air at an initial pressure p 1= 1.10 x 10 5 Pa and temperature T 1 = 300 K. Assume that air behaves like ideal gas. The graph below shows a sequence o f changes imposed on the air in cylinder. (a) AB – the air heated to 375 K at constant pressure. Calculate the new volume, V2. (b) BC – the air is compressed isothermally to volume V 1. Calculate the new p1 T1 piston V1 V2 p1 p2 pressure/ Pa volume/ cm3 A B C 0

4 Topic 9: First Law of Thermodynamics Page 4 9749 H2 Physics Tutorial pressure, p2. [1.25 x 10-3 m3, 1.37 x 105 Pa] 11. The gas in the cylinder of a diesel engine can be considered to undergo a cycle of changes of pressure, volume and temperature. One such cycle, for an ideal gas, is shown on the graph. (i) The temperature of the gas at A and B are 300 K and 660 K respectively. Use the ideal gas equation and data from the graph to find the temperatures at C and D. (ii) During each of the four section s of the cycle, changes are being made to the internal energy of the gas. Some of the factors affecting these changes are given in the table below. Explain why the wo rk done on the gas is sometimes negative and find the work done on the gas in section D to A. Deduce the valu es of the “increase in internal energy of the gas” for each section and list them. 1.0x105 7.8x105 16x105 1.40x10-4 6.00x10-4 10.0x10-4 Pressure/Pa Volume/m3 Section of cycle Heat supplied to gas / J Work done on gas/J Increase in internal energy of gas/J A to B 0 300 B to C 2580 -740 C to D 0 -440 D to A -1700

5 Topic 9: First Law of Thermodynamics Page 5 9749 H2 Physics Tutorial 12 N08/III/4(b) An ideal gas undergoes a cycle of changes A B C A, as shown in Figure 4.1. Figure 4.1 (i) Calculate the work done by the gas during the change C A. [2] (ii) Figure 4.2 is a table of energy changes during one cycle. Complete figure 4.2. Figure 4.2 13 A fixed mass of gas in a heat pump undergoes a cycle of changes of pressure, volume and temperature as shown below. The gas is assumed to be ideal. The following table shows an increase in internal energy which takes place during each of the changes A to B, B to C and C to D. It also shows that in both of sections A to B and C to D, no heat is supplied to the gas. Using the first law of thermodynamics and other necessary data from the graph, complete the table above.     Increase in Internal energy/J Heat supplied to gas/J Work done on gas/J A to B 1200 0 B to C - 1350 -1350 C to D - 600 0 D to A

6 Topic 9: First Law of Thermodynamics Page 6 9749 H2 Physics Tutorial 14 In the proces s illustrated by the pV diagram in Figure 2, the temperature of the ideal gas remains constant at 85.0 oC. Figure 2 (a) How many moles of gas are involved? (b) What volume does this gas occupy at a? (c) How much work was done by or on the gas from a to b? (d) By how much did the internal energy of the gas change during this process? 15 The graph in Figure 3 shows a pV diagram for 3.25 moles of ideal helium (He) gas. Part ca of this process is isothermal. Figure 3 (a) Find the pressure of the Heat point a. (b) Find the temperature of the He at points a, b and c. (c) How much heat entered or left the He during segments ab, bc and ca? In each did heat enter or leave? (d) By how much did the internal energy of the He change f