This preview shows pages 1–2. Sign up to view the full content.
S37.
Calculate
W
and
Q
for each of the four steps of a Carnot cycle applied to 1 mole of an ideal gas.
Divide the
expression that you obtain for total
W
by
Q
2
, and compare the result with 
W
/
Q
2
= (T
2
T
1
)/T
2
to show that
temperatures on the ideal gas scale (those used in your calculation) are proportional to those on the thermodynamic
scale (those used in the equation above).
By choosing the size of the degree to be the same, the two scales become
identical.
The Carnot cycle consists of 4 steps.
We need to calculate W and Q for each step and
then sum them together to find the total heat and work.
Step 1 Isothermal expansion
W
=
−
nRT
2
ln
V
2
V
1
⎛
⎝
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
Q
=
nRT
2
ln
V
2
V
1
⎛
⎝
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
Step 2: Adiabatic expansion
W
=
nC
v
Δ
T
=
n
3
2
R
(
T
1
−
T
2
)
Q
=
0
Step 3: Isothermal compression
W
=
−
nRT
1
ln
V
4
V
3
⎛
⎝
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
Q
=
nRT
1
ln
V
4
V
3
⎛
⎝
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
Step 4: Adiabatic compression
W
=
nC
v
Δ
T
=
n
3
2
R
(
T
2
−
T
1
)
Q
=
0
Because the process is cyclic,
Δ
U
=
0
and
W
tot
=
−
Q
tot
.
Adding up the work for each of the four steps gives
W
tot
=
−
RT
2
ln
V
2
V
1
⎛
⎝
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
+
3
2
R
(
T
1
−
T
2
)
−
RT
1
ln
V
4
V
3
⎛
⎝
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
+
3
2
R
(
T
2
−
T
1
)
=
−
RT
2
ln
V
2
V
1
⎛
⎝
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
−
RT
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/01/2011 for the course CHEM 111 taught by Professor Owens,g during the Fall '08 term at University of Utah.
 Fall '08
 Owens,G
 Mole

Click to edit the document details