Chemistry 231
Tutorial Session 3
G. Marangoni
Date: Friday, October 24, 2008.
The following questions will be answered on the tutorial session.
1. Calculate the efficiency of the following process.
a. A Carnot engine operating between 520K and 298 K.
b. A Carnot refrigerator operating between -5C and 30C.
c. An air conditioning system operating between 5C and 32C.
d. A heat pump operating between -10C and 22C.
2. A Carnot engine, containing 497 kPa of an ideal gas (Cv,m = 5/2 R, V1 = 1.50 L) as the
working fluid, operates between 640 K and 300 K. Assuming that the volume on the
downstroke of the engine is 4.0L, calculate q, w, U and H for each step in the process.
Please answer the following questions. Answers will be posted on the website.
3. An automobile engine operates between 600C and 298 K. The enthalpy of combustion
of iso-octane (gasoline) is 2.23 kJ/g and its density is 0.78 g/mL.
a. Calculate the Carnot efficiency of an engine.
b. Calculate the overall efficiency of the engine if it 40% of its Carnot efficiency.
c. For the real auto engine, calculate the amount of gasoline (in L/h) required to do
905W of work.
4. The Chalk Point Maryland Power station has a gross electrical generating capacity of 710
MW. At a steam pressure of 3600 psi, the outlet temperature at the super-exchanger is
540C, and the condensate temperature is 30C.
a. Calculate the Carnot efficiency of the generating station.
b. If the boiler efficiency is 91.4% and the turbine efficiency is rated at 46.7% (note
this includes the Carnot efficiency and mechanical losses), and the generator is
98.4%, what is the overall efficiency of the plant?
c. One of the coal burning units in this plant produces 355 MW of power. How
many metric tons of coal are required per hour are required to fuel the unit (note –
the heat of combustion of coal is 29.0 MJ/Kg).
d. How much heat is rejected to the cold temperature reservoir per minute?
e. Assume that 960 000 L of water pass through the condenser in a minute.
Calculate the temperature rise in the water (note for H2O, Cp = 4.184 J/(g K)).
Answers
1.
a. For a Carnot engine
Tc
Th
298K
1
520K
C  1 
 0.427
b. For a Carnot refrigerator
Tc
r 
Th Tc
268K

303  268K
 7.66
c. Treat the air conditioning systems as a Carnot refrigerator
r 

Tc
Th Tc
278K
305  278K
 10.3
d. For a Carnot heat pump
 hp 
Th
Th Tc
295K

295  263K
 9.22
2. For the Carnot engine operating between 640 K and 300 K
Tc
Th
300K
1
640K
C  1 
 0.531
Step 1 - Isothermal, reversible expansion
U1 = H1 = 0; q1 = -w1.
V 
w 1  nRT ln 2 
V 1 
J
 4.0L 
x 640Kx ln

Kmole
 1.5L 
 731J
 q 1  731J
 0.140molex 8.314
Step 2 – Ideal gas, adiabatic, reversible expansion
U2 = w2; q2 = 0.
U2 = nCv,mT = 0.140 mole x 5/2 x 8.314 J/(K mole) x (-340 K)
= -990 J = q2
H2 = nCp,mT = 0.140 mole x 7/2 x 8.314 J/(K mole) x (-340 K)
= -1385 J
Step 3 - Isothermal, reversible compression
U3 = H3 = 0; q3 = -w3.
V 
w 3  nRT ln 2 
V 1 
J
 1.50L 
 0.140molex 8.314
x 300Kx ln

Kmole
 4.00L 
 342J
 q 3  342J
Step 4 – Ideal gas, adiabatic, reversible compression
U4 = w4; q4 = 0.
U4 = nCv,mT = 0.140 mole x 5/2 x 8.314 J/(K mole) x (340 K)
= +990 J = q4
H4 = nCp,mT = 0.140 mole x 7/2 x 8.314 J/(K mole) x (340 K)
= +1385 J
Note for the cycle
qcycle = q1 + q2 + q3 + q4
= 731 J-342 J
= 389 J
wcycle = -qcycle
= -389 J
Note
w cy cle
Tc

Th
q1
389J

731J
C  1 
 0.532
3. Calculate the efficiency as if the engine operate as a Carnot Engine
a. For a Carnot engine
T
C  1 c
Th
298 K
873K
 0.656
 1
b. For a real engine with an efficiency 40% of that of the Carnot engine
 C   C  0.40
 0.656  0.40
 0.263
c. For the real engine, in order to do 905 W of work.
w
 C   cycle
q1
905 J s 1
 0.263 
q1
905 J s 1
0.263
 3435 J s 1
 q1 
 C  
wcycle
q1
905 J s 1
 0.263 
q1
905 J s 1
0.263
 3435 J s 1
 q1 
For one hour – the heat required is 1.237 x 107 J, or 1.237 x 104 kJ
The mass of fuel required.
1.237 104 kJ
g of fuel 
2.23kJ g 1
 5.543 103 g of fuel
5.543 103 g
0.78 g mL1
 7109 mL
 7.11L
mL of fuel 
4. Calculate the efficiency of the boiler system
a. Carnot efficiency
T
C  1 c
Th
303K
813K
 0.627  62.7%
 1
b. To obtain the overall efficiency, we have to multiply turbine efficiency (which is
a composite of the ideal, Carnot efficiency and frictional and other mechanical
losses) by the boiler and the generator efficiency

 overall
  C   B   G
 0.467  0.914  0.984
 0.467  0.899
 0.420  42.0%
c. To produce 355MW of power.

 overall

 0.420 
wcycle
q1
355 106 J s 1
q1
355 106 J s 1
0.420
 845 106 J s 1
 The amount of coal per second is
Kg coal = 845 MJ s-1 / 291 MJ kg-1
= 29.1 kg s-1
 q1 
For one hour – the amount required is 29.1 kg s-1 x 3600 s
= 105 Mg h-1
= 105 metric tonnes
d.
Note
q1  q3   wcycle
 q3   q1  wcycle
 845MJ   355MJ 
 q3  490 MJ  4.90 108 J
e.
Note – for one minute
 q3  490MJ s 1  4.90 108 J s 1  60 s
 2.94 1010 J
96000 L  9.60 108 g
q3
 T 
mH 2O  4.184 J g 1K 1

2.94 1010 J
 7.2 K  7.2 oC
8
1 1
9.60 10 g  4.184 J g K