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

.