Universe entropy variation of one body and a reservoir

[Sabian]

Homework Statement

One body of constant pressure heat capacity C_P at temperature T_i it's placed in contact with a thermal reservoir at a higher temperature Tf. Pressure is kept constant until the body achieves equilibrium with the reservoir.
a) Show that the variation in the entropy of the universe equals:
C_P [x − ln(1 + x )],
onde x = − \frac {(Tf− Ti )}{Tf}

(There might be some translation issues from Portuguese to English).

Homework Equations

All I can think is
C_P= T \left ( \frac {\partial S}{\partial T} \right )_P
dU = T dS
dQ = C_P dT
dS = \frac {dQ}{T}

The Attempt at a Solution

I haven't been able to understand the underlying physics properly. I attempted a "no idea what I'm doing but here I go" with the first equation, which led to nothing. I assume that the entropy variation of the universe should be the addition of the variation in the body and in the reservoir but can't seem to calculate them correctly.Thank you for your time people.

 

[Sabian]

I know it's rude to bump threads, but does anybody have the time and knowledge to help me?

 

[Chestermiller]

I know it's rude to bump threads, but does anybody have the time and knowledge to help me?

To get the total entropy change for the combination of system and surroundings, you have to take each of them separately along reversible paths from the initial to the final state. Can you think of a reversible path between the initial and final state for the system? Can you think of a reversible path between the initial and final state for the reservoir? How much heat is transferred between the system and the reservoir when it goes from the initial to the final state? All this heat is transferred to the reservoir at its (constant) temperature T_f.

That's all the hints I can give you without revealing every last detail.

 

[Sabian]

I could figure it out, thanks man, really.