10.2 Problems
423
10.50 (a) Write down the efficiency for a Carnot cycle as a function of
(i) the heat flows to and from the reservoirs and
(ii) the temperatures of the two reservoirs.
(b) Describe the working of an Otto engine and efficiency for the air standard Otto cycle as a function of temperature as well as volume. Start by
sketching this cycle in a standard P–V diagram. Explain the four steps
of this cycle in terms of associated temperature and volume changes as
well as the heat exchanged with external reservoirs.
(c) Compare the Carnot and the Sterling cycle using P–V diagram.
10.51 (a) 1 × 10 −3 m 3 of He at normal conditions ( p 0 = 1 bar, T 0 = 0 ◦ C) is
heated to a final temperature of 500 K. What is the entropy change for
(i) an isobaric and
(ii) an isochoric process?
Use C P
He = 21 J/(mol K) and C V
He = 12.7/(mol K).
(b) Calculate the change in entropy S 1 for 1 kg of water being heated from
0 to 50 ◦ C. Compare this change in entropy S 2 for 0.5 kg of water at
0 ◦ C being mixed with 0.5 kg of water at a temperature of 100 ◦ C. Use
C V
H 2 O = 4.13 × 10 3 J/(kg K).
10.52 Consider a reversible isothermal expansion of an ideal gas in contact with the
reservoir at temperature T , from an initial volume V 1 to a final volume V 2 .
(a) What is the change in the internal energy of the system?
(b) Calculate the work done by the system.
(c) What is the amount of heat absorbed by the system?
(d) Find the change of entropy of the system.
(e) Find the change of the entropy of the system plus the reservoir.
10.53 Internal energy, heat, enthalpy, work, and the Gibbs free energy (Gibbs function) are all measured in units of joules.
(a) What is the difference between these forms of energy? Write down the
equations relating these forms of energy.
(b) Which of the above are state variables? What properties distinguish a
state variable from other variables?
10.2.6 Elasticity
10.54 (a) A 100 MPa force is applied to the surface of a material (surface area,
1 m 2 ) that exerts a shear across the material (Fig. 10.4). The sample has
a thickness of 10 cm and causes the surface to be displaced by 0.1 cm.
What is the shear modulus of the material?
423
10.50 (a) Write down the efficiency for a Carnot cycle as a function of
(i) the heat flows to and from the reservoirs and
(ii) the temperatures of the two reservoirs.
(b) Describe the working of an Otto engine and efficiency for the air standard Otto cycle as a function of temperature as well as volume. Start by
sketching this cycle in a standard P–V diagram. Explain the four steps
of this cycle in terms of associated temperature and volume changes as
well as the heat exchanged with external reservoirs.
(c) Compare the Carnot and the Sterling cycle using P–V diagram.
10.51 (a) 1 × 10 −3 m 3 of He at normal conditions ( p 0 = 1 bar, T 0 = 0 ◦ C) is
heated to a final temperature of 500 K. What is the entropy change for
(i) an isobaric and
(ii) an isochoric process?
Use C P
He = 21 J/(mol K) and C V
He = 12.7/(mol K).
(b) Calculate the change in entropy S 1 for 1 kg of water being heated from
0 to 50 ◦ C. Compare this change in entropy S 2 for 0.5 kg of water at
0 ◦ C being mixed with 0.5 kg of water at a temperature of 100 ◦ C. Use
C V
H 2 O = 4.13 × 10 3 J/(kg K).
10.52 Consider a reversible isothermal expansion of an ideal gas in contact with the
reservoir at temperature T , from an initial volume V 1 to a final volume V 2 .
(a) What is the change in the internal energy of the system?
(b) Calculate the work done by the system.
(c) What is the amount of heat absorbed by the system?
(d) Find the change of entropy of the system.
(e) Find the change of the entropy of the system plus the reservoir.
10.53 Internal energy, heat, enthalpy, work, and the Gibbs free energy (Gibbs function) are all measured in units of joules.
(a) What is the difference between these forms of energy? Write down the
equations relating these forms of energy.
(b) Which of the above are state variables? What properties distinguish a
state variable from other variables?
10.2.6 Elasticity
10.54 (a) A 100 MPa force is applied to the surface of a material (surface area,
1 m 2 ) that exerts a shear across the material (Fig. 10.4). The sample has
a thickness of 10 cm and causes the surface to be displaced by 0.1 cm.
What is the shear modulus of the material?