Question

QUESTION 1

2n molecules of nitrogen gas and 6n molecules of hydrogen gas are inside a container and separated from each other by a valve. The entire container is thermally and mechanically isolated from the rest of the universe. The gases are initially at the same temperature, 300 K. If the value is opened, the gases interact with each other to form ammonia (NH₃). What is the final temperature (in K) of the system if n molecules of ammonia are formed? You can treat the gases as ideal with heat capacities (C= 5/2 NKb) for N₂ and H₂ and (C=3 NKb) for ammonia.

Answer 1

According to conservation of energy (U = f/2 Nk_B T) U_1 + U_2 = U [5/2(2n) + 5/2(6n)]k_B T = 6/2 n K_B T^prime (5 + 15) times 300 = 3T^prime T^prime = 20 times 100 T^prime = 2000 K