Question

Equal masses of methane at 300K and ethylene at 600 K are mixed such that the pressure is cosntant, and no heat can escape. What will be the final temperature? Use te heat capacities of Table 2.1 assuming them constant.

Cvm=27.07 CH4

Cvm=33.56 C2H4

Answer 1

Let "T" be final mixturetemperature. Heat energy gained by methane
(with initial temp 300 degK) must equal heat energy lost by ethylene.
(with initial temp 600 degK), so that we have following equation which can be solved for "T":

     (1 mole)*(C_P:methane)*(T- 300) = (1mole)*(C_P:ethylene)*(600 - T)

     ---->    (1)*(27.07)*(T - 300) = (1)*(33.56)*(600 - T)

     ---->   {Final Temp} = T = 466 K