HOMEWORK ASSIGNMENT 5
Problems Chapter 5
5-2
The internal energy of an ideal gas is
u = u0 + cv (T − T0 ) .
a)
Show that the Joule coefficient η = 0.
µ
¶
µ
µ
¶¶
∂T
∂ u − u0
η=
=
=0
∂v u
∂v
cv
u
b)
Show that the Joule-Thompson coefficient µ = 0.
h = u + P v = u0 + cv (T − T0 ) + nRT
µ
¶
µ
µ
¶¶
∂T
∂
h − u0 + cv T0
µ=
=
=0
∂P h
∂P
cv + nR
h
5-7
50 kg of water at 0 0 C is frozen in a refrigerator operating in a room at
0
20 C. The latent heat of fusion is 3.33 ∗ 105 J/kg. What is the power required
to freeze the water in one hour?
∆h = ∆u + P ∆v = ∆u = 3.33 ∗ 105
∆u
3.33 ∗ 105
= 50 ∗
= 4625
∆t
3600
The coefficient of performance is
c=
273.15
= 13. 66
20
so the power required is
power =
5-8
4625
= 339
13. 66
The efficiency for a Carnot engine is
η =1−
Which is greater
η1 = 1 −
T1
T2 + ∆
η2 = 1 −
T1 − ∆
.
T2
or
Answer
T1
T2
1−
η1
=
η2
1−
T1
T2 +∆
T1 −∆
T2
1
=
T2
< 1.
T2 + ∆