Entropy/ 2nd law of thermodynamics

[BingoMan]

Homework Statement

A mass of water at T1 is isobarically and adiabatically mixed with an equal mass of water at T2. Show that the entropy change in the universe is 2*m*Cp*ln[(T1 + T2)/(2*SQRT(T1*T2))]

Homework Equations

I'm assuming
dS = dq/T
q = m Cp dT

The Attempt at a Solution

At the very beginning I was just using q = cpdT and getting total entropy = to m Cp ln(T2/T1) but that might be because that takes the process as reversible and this is an irreversible function

Next, I tried to find the equilibrium temperature by setting q1(using T1 and Tf) and q2 (using T2 and Tf) = 0 but I don't believe that is true and I couldn't figure out a way to get the equation given in the question.

It seems like it would be simple but I must be missing something.

Please help

 

[BingoMan]

Is this answer as simple as finding the equilibrium temperature then using that to find the entropy change in both masses and subtracting those?? If that's the case, then how does one figure out the equilibrium temp because I tried that to no avail.

 

[Andrew Mason]

Homework Statement

A mass of water at T1 is isobarically and adiabatically mixed with an equal mass of water at T2. Show that the entropy change in the universe is 2*m*Cp*ln[(T1 + T2)/(2*SQRT(T1*T2))]

Homework Equations

I'm assuming
dS = dq/T
q = m Cp dT

The Attempt at a Solution

At the very beginning I was just using q = cpdT and getting total entropy = to m Cp ln(T2/T1) but that might be because that takes the process as reversible and this is an irreversible function

Next, I tried to find the equilibrium temperature by setting q1(using T1 and Tf) and q2 (using T2 and Tf) = 0 but I don't believe that is true and I couldn't figure out a way to get the equation given in the question.

It seems like it would be simple but I must be missing something.

Is this answer as simple as finding the equilibrium temperature then using that to find the entropy change in both masses and subtracting those?? If that's the case, then how does one figure out the equilibrium temp because I tried that to no avail.

It is not a simple question.

I think you are expected to take into account the vapour pressure of the water and assume that it is saturated at all times.

AM

 

[BingoMan]

I thought I might have to do that but it is isobarically mixed so I do not know how to deal with that