Question

Two different gases A and B are mixed. Calculate change of entropy.
a) Assume pressure and temperature of A and B are the same.
b) Now assume pressure and temperature of A and B are different. The system is
thermally isolated. Calculate entropy and final temperature, Tf.

Answer 1

a)

When temperature and pressure are same

where V₂ is the final volume and V₁ is the initial volume

Now, for each gas, the volume V₁ is the initial volume of the gas, and V₂ is the final volume, which is both the gases combined, V_A+V_B. So for the two separate gas expansions, we have

Similarly,

Adding the above two we get,

Now, using PV = nRT we have V is proportional to 'n' since all other parameters are constant, we have

where x_A and x_B are mole fractions

Please split the second question