47. When the temperature changes by ∆T the internal energy of the first gas changes by n
1
C
1
∆T , the
internal energy of the second gas changes by n
2
C
2
∆T , and the internal energy of the third gas changes
by n
3
C
3
∆T . The change in the internal energy of the composite gas is ∆E
int
= (n
1
C
1
+n
2
C
2
+n
3
C
3
) ∆T .
This must be (n
1
+ n
2
+ n
3
)C ∆T , w here C is the molar specific heat of the mixture. Thus
C =
n
1
C
1
+ n
2
C
2
+ n
3
C
3
n
1
+ n
2
+ n
3
.