Question

Suppose 2 moles of helium gas at 200K are mixed with 2 moles of krypton gas at 400K in a calorimeter. What is the final temperature?

Answer 1

Thermal energy of gas = n C_v T

where n is number of moles , C_v is specific heat at constant volume and T is temperature of gas .

In the given mixture of monoatomic gases, both gases have equal number of moles and their specific heats at constant volume are same. Hence equal thermal energy gained or lost from respective gas and the temperature of mixture will be intermediate value 300 K as explained below

n C_v ( 400 - T ) = n C_v (200 + T )

from above equation we get T = 100 K

Hence final temperature T = ( 400 - T ) = (200 + T ) = 300 K