PHGN341: Thermal Physics
Exam II - April 12, 2013
NAME:
1. (30) A nuclear power plant generates 3 GW (3 × 109 W) of electricity by operating on a Rankine cycle (steam engine)
between {T1 = 20 C,P1 = .023 bar} and {T3 = 600 C, P3 = 300 bar}. (The steam tables are attached.)
2
(a) What is the enthalpy of 1 kg of water after the turbine power step (3 → 4)?
3
Pressure
(Steam)
(Water)
1
(Water + Steam)
4
Volume
(b) Suppose the plant operates at an efficiency of 48%, what is the minimum mass of water that must pass through the
generating plant turbines per second to generate 3 GW electric power?
(c) The waste heat is dumped into a nearby river which has a flow rate of 2 × 105 kg per second. Upstream from the
plant the temperature of the river water is 20 C. What is the average temperature of the river water downstream from
the plant? (The heat capacity of water at constant pressure is cp = 4.18 kJ/(kg-K).)
1
2. (20) Estimate the temperature of the melting point of ice at 200 bar pressure. (Data: Latent heat: L = 0.333 MJ/kg,
upon freezing 1000 cm3 of water (1 kg) expands to 1091 cm3 .)
3. (20) A methane (CH4 ) fuel cell operates by combining oxygen and methane to form water (liquid) carbon dioxide
at standard pressure and temperature with the transfer of 4 electrons per molecule of water formed: CH4 + 2O2 →
2H2 O + CO2 .
Table 1: Thermodynamic properties per mole of substance.
Substance ∆f H (kJ) ∆f G (kJ) S (J/K) CP (J/K)
H2 O (l)
-285.83
-237.13
69.91
75.29
O2 (g)
0.0
0.0
205.14
29.38
CH4 (g)
-74.81
-50.72
186.26
35.31
CO2 (g)
-393.51
-394.36
213.74
37.11
a. Calculate the voltage of a methane fuel cell?
b. How much heat is delivered to the environment per mole of water produced?
2
4. (30) Consider an ideal gas consisting of N indistinguishable (massless) neutrinos at temperature, T , confined to an
area, A. The neutrino’s kinetic energy is given by the ultrarelativistic relation: E = pc where c is the speed of light.
A
2
(Recall that the particle-in-a-box result for the density of states in 2 dimensions is d2 n = (2πh̄)
2 d p.)
(a) Calculate the partition function for a single neutrino confined to area, A.
(b) Calculate the average energy of one neutrino in two dimensions.
(c) What is the partition function for the N-neutrino gas in terms of the single neutrino partition function?
(d) Use your result from part (c) to calculate the 2-dimensional analog of the “pressure” (force per unit length along
the boundary of the confining area) for the neutrino gas.
3
Steam Tables
T (◦ C)
0
10
20
30
50
100
P (bar)
0.006
0.012
0.023
0.042
0.123
1.013
Hwater (kJ)
0
42
84
126
209
419
Hsteam (kJ)
2501
2520
2538
2556
2592
2676
Swater (kJ/K)
0
0.151
0.297
0.437
0.704
1.307
Ssteam (kJ/K)
9.156
8.901
8.667
8.453
8.076
7.355
Table 1. Thermodynamic properties of 1 kg of saturated water/steam.
P
1.0
3.0
10
30
100
300
Property
H (kJ)
S(kJ/K)
H (kJ)
S(kJ/K)
H (kJ)
S(kJ/K)
H (kJ)
S(kJ/K)
H (kJ)
S(kJ/K)
H (kJ)
S(kJ/K)
200 C
2875
7.834
2866
7.312
2828
6.694
300 C
3074
8.216
3069
7.702
3051
7.123
2994
6.539
400 C
3278
8.544
3275
8.033
3264
7.465
3231
6.921
3097
6.212
2151
4.473
Table 2. Thermodynamic properties for 1 kg of superheated steam.
4
500 C
3488
8.834
3486
8.325
3479
7.762
3457
7.234
3374
6.597
3081
5.791
600 C
3705
9.098
3703
8.589
3698
8.029
3682
7.509
3625
6.903
3444
6.233