Question

Two systems of monotonic ideal gas are separated by a diathermal wall. In system A there are 2 moles initially at 175 K, in system B there are 3 moles initially at 400 K. Write U_AUA​ and U_BUB​ as functions of RR and the determine the common temperature (in Kelvin) after equilibrium is reached.​

Answer 1

Answer:

Explanation:

Net P-V work done=0 as no net change in volume takes place.

Also net heat absorbed= 0

Thus by first law, net internal energy change=0

⇒n  

1

​  

C  

v  

1

​  

 

​  

ΔT  

1

​  

+n  

2

​  

C  

v  

2

​  

 

​  

ΔT  

2

​  

=0

Both gases are monoatomic ⇒C  

v  

1

​  

 

​  

=C  

v  

2

​  

 

​  

=  

2

3

​  

R

Let final temperature of mixture at equilibrium be T

Then  

2

3

​  

R(n  

1

​  

(T−T  

1

​  

)+n  

2

​  

(T−T  

2

​  

))=0⇒T=  

n  

1

​  

+n  

2

​  

 

n  

1

​  

T  

1

​  

+n  

2

​  

T  

2

​  

 

​