Download Problem Set 5 - 2004

2TP - Thermal Physics
Department of Physics, University of Surrey
Problem Set 5:
Entropy
You should read Chapter 5 of Thermal Physics by C.B.P. Finn, if you have not already.
(1) For each of the following processes, state whether the entropy is increasing,
decreasing or staying the same.
(i) A piston filled with an ideal gas is surrounded by very good thermal insulation. It is
compressed slowly. How does the entropy of the gas change?
(ii) The insulation is removed from around the piston, and its diathermal walls are
exposed to the surrounding atmosphere of the room. The piston is compressed slowly so
as to maintain a constant temperature of the gas. How does the entropy of the gas
change?
(iii) A pail of warm water is placed outside on a winter’s night so that it cools by about
30 C. What is the entropy change of the water? What is the entropy change of the
thermodynamic universe consisting of the water and the surrounding atmosphere?
(iv) A shopping trolley moving at a constant velocity hits a brick wall and comes to a
stop. What is the entropy change of the universe?
(v) A block of steel slides across a large wooden floor and comes to rest solely as a result
of friction.
(2) A warm block of lead, weighing 2 kg and at a temperature of 50 C, is tossed into a
cool lake at a temperature of 10 C. The block cools to the temperature of the lake.
(i) What is the entropy change of the block?
(ii) What is the entropy change of the lake?
(iii) What is the entropy change of the thermodynamic universe consisting of the block
and the lake?
You can use the Dulong-Petit law to estimate that the specific heat capacity of lead is
equal to 3R, which is the value approached by solids at high temperatures. The atomic
weight of lead is 207.2 g mol-1.
(3) Two moles of an ideal gas at T = 400 K expand quasi-statically and isothermally
from an initial volume of 30 L to a final volume of 90 L. What is the entropy change of
the gas as a result of the expansion? What is the entropy change of the thermodynamic
universe?
For discussion during Tutorial 5 in Week 10 on 7 December, 2011
2TP - Thermal Physics
Department of Physics, University of Surrey
(4) At low temperatures, the molar specific heat of diamond varies with temperature as:
3
T 
c v  1.94  10   ,
 
3
(J mol-1 K-1)
where the Debye temperature, , is 1860 K. What is the entropy change of a 1 mg
diamond crystal when it is heated at constant volume from a temperature of 4 K to 300
K? The atomic weight of carbon (which is the only element that makes up diamond) is
12.01 g mol-1.
(5) An electric current of 10 A is passed through a 5- resistor in a thermally isolated
box. The initial temperature of the resistor is 20 C, and its heat capacity is 4 JK-1.
Assuming that the electrical energy is completely converted to heat, what is the change in
entropy of the resistor during the first second that the current flows? Will the entropy
change be the same over the next second?
(6) Sketch a plot of temperature versus entropy for a Carnot cycle and briefly describe
each of the four processes in terms of temperature and entropy changes.
(7) A heat engine absorbs heat from a reservoir at 300 K and rejects heat reversibly to a
reservoir at 200 K. The engine has an efficiency of 25% as it does125 J of work. What is
the entropy change of the engine during one cycle? What is the entropy change of the
universe?
For discussion during Tutorial 5 in Week 10 on 7 December, 2011