Internal Energy

24. A sample of helium behaves as an ideal gas as energy is added by heat at constant pressure from 273 К to 373 K. If the gas does 20.0 J of work, what is the mass of helium present?

25. One mole of an ideal gas is heated slowly so that it goes from p-V

state ( ) to ( ) in such a way that the pressure of the gas is directly proportional to the volume, (a) How much work is done in the process? (b) How is the temperature of the gas related to its volume during this process? (Ans. (a) )

26. An ideal gas is enclosed in a cylinder with a movable piston on top. The piston has a mass of 8 000 g and an area of 5.00 cm² and is free to slide up and down, keeping the pressure of the gas constant. How much work is done as the temperature of 0.200 mol of the gas is raised from 20.0°C to 300°C? (Ans. 466J)

27. A gas is compressed from 9.00 L to 2.00 L at a constant pressure of 0.800 atm. In the process, 400 J of energy leaves the gas by heat, (a) What is the work done by the gas? (b) What is the change in its internal energy?

28. A thermodynamic system undergoes a process in which its internal energy decreases by 500 J. If, at the same time, 220 J of work is done on the system, what is the energy transferred to or from it by heat? (Ans. -720 J)

29. A gas in a cylinder is cooled and compressed at a constant pressure of 2.0 x 10⁵ Pa, from 1.2 m³ to 0.8 nr. A quantity of heat of magnitude 2.4 x 10³ J is removed from the gas.

a)Find the work done by the gas.

b)Find the change in internal energy of the gas.

c)Does it matter whether or not the gas is ideal?

30. When a system is taken from state a to state b, in Fig. 18-S, along the path acb, 80 J of heat flow into the system, and 30 J of work are done.

a)How much heat flows into the system along path adb if the work is 10 J? (Ans. 60 J)

When the system is returned from b to a along the curved path, the magnitude of the work is 20 J. Does the system absorb or liberate heat, and how much? (Ans. 70 J liberated)

c)If U_a = 0 and U_d = 40 J, find the heat absorbed in the processes ad and db. (Ans. ad 50 J db 10 J )

34. A 2.00-mol sample of helium gas initially at 300 К and 0.400 atm is compressed isothermally to 1.20 atm. Assuming the behavior of helium to be that of an ideal gas, find (a) the final volume of the gas, (b) the work done by the gas, and (c) the energy transferred by heat. (Ans. (a) 0.041 m³, (b) -5.48 kJ, (c) -5.48 kJ)

35. One mole of an ideal gas, initially at 300 K, is cooled at constant volume so that the final pressure is one-fourth the initial pressure. The gas then expands at constant pressure until it reaches the initial temperature. Determine the work done by the gas. (Ans. 1.87 kJ)

36. One mole of an ideal gas is contained in a cylinder with a movable piston. The initial pressure, temperature, and volume are and ,

respectively. Find the work done by the gas for the following processes: (a) An isobaric compression in which the final volume is one-half the initial volume, (b) An isothermal compression in which the final pressure is four times the initial pressure, (c) An isovolumetric process in which the final pressure is triple the initial pressure.

37. A ideal gas is compressed from 0.080 m³ to 0.065 m³ at a constant pressure of 8.0x10 Pa. Calculate

1. the work done on the gas;

2. the change in the internal energy of the gas.

43. An ideal gas in a cylinder is compress constant temperature from a volume at pressure to a volume , at pressure . Which of the following is true?

A Heat is lost by the gas.

В Internal energy of the gas increases.

С Work is done by the gas.

D Work done on the gas is

44. When an ideal gas undergoes an isothermal change,

A. the number of degree of freedom changes.

B. temperature of the gas changes.

C. there is no heat transfer with the surrounding. D the internal energy of the gas remains constant.

45. One mole of an ideal gas expands isothermally at temperature T until its volume is 3 times of its initial volume. If R is the molar gas constant, work done by the gas is

A 3RT В 3RTlnV С RTlnV D 3/2RT.

46. One mole of an ideal gas is in a cylinder fitted with a frictionless piston. The initial temperature of the gas is T. The gas is heated at constant energy, and W the work done by the system. Explain the sign convention you use.

(b) For a system consisting of a real gas,

(i) What forms the internal energy?

(ii) Give an example of external work done on the system.

53. An ideal gas initially at 10 atm and 300 К is permitted to expand adiabatically until its volume doubles. Find the final pressure and temperature if the gas is

a)monatomic;

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b)diatomic.

56. During an adiabatic expansion, the temperature of 0.1 mol of oxygen drops from 30°C to 10°C.

a)How much work does the gas do? (Ans. 42.2 J)

b)How much heat is added? (Ans. 0)

57. An ideal gas expands slowly to twice its original volume, doing 500 J of work in the process. Find the heat added and the change in internal energy if the process is a) isothermal; (Ans. a) 500 J, 0) b) adiabatic. (Ans. 0, -500 J)

58. In a cylinder, 2.0 mol of an ideal monatomic gas initially at 1.0 x 10⁶ Pa and 300 К expands until its volume doubles. Compute the work done if the expansion is

a) isothermal; b) adiabatic; c) isobaric.

d)Show each process on a pV-diagram.

e)In which case is the magnitude of the heat transfer greatest? Least?

f) In which case is the magnitude of the internal-energy change greatest? Least?

59. Two moles of helium are initially at a temperature of 27^CC and occupy a volume of 0.020 m³. The helium first expands at constant pressure until the volume has doubled, and then adiabatically until the temperature returns to its initial value.

a) Draw a diagram of the process in the p-V -plane.

b)What is the total heat supplied in the process? (Ans. 1.25x10 J)

c)What is the total change in the internal energy of the helium? (Ans. 0)

d)What is the total work done by the helium? (Ans. 1.25x10⁴ J) e) What is the final volume? (Ans. 0.112 m³ J)

Heat Capacities

61. A cylinder contains 1 mol of oxygen gas at a temperature of 27°C. The cylinder is provided with a frictionless piston, which maintains a constant pressure of 1 atm on the gas. The gas is heated until its temperature increases to 127°C.

b)How much work is done by the gas in this process? c)On what is this work done? d)What is the change in internal energy of the gas? e)How much heat was supplied to the gas? f)How much work would have been done if the pressure had been 0.5 atm?

62. A certain ideal gas has -1.33. Determine the molar heat capacities at constant volume and at constant pressure. (Ans. Cy - 25.2(J/mol -K), Cp=33.5(J/mol-K))

65. During the compression of a sample of an ideal gas at constant pressure, 320 J of work is done on the gas and it is found that the temperature of the gas decreases by 8 К If the heat capacity at constant volume cy for this sample is 100 J/K, calculate

1. the change in the internal energy of the gas

2. the amount of heat dissipated from the gas.

3. the heat capacity at constant pressure Cp for this sample.

66. The heat required to raise the temperature of a sample of an ideal gas by 10 К at constant pressure is 1743 J and at constant volume is 1245 J. Calculate the gas the number of moles in the sample.

78. One mole of a monatomic ideal gas is held in a cylinder with a frictionless piston. When 63 J of heat is supplied and the gas is allowed to expand at constant pressure, the temperature increases by 3.0 K. How much heat input will be required for the same increase in the temperature of this gas if the volume is fixed?