Thermodynamics - obtaining quenching entropy

[mouser]

I'm having a problem determining the total entropy change in a metal quenching problem. Here is the information I am given (subscript 'm' is for metal, 'w' is water):

m_m = 20 kg
m_w = 1000 kg
T_1m = 800 C
T_1w = 30 C
C_pm = .4 kJ/kg K
C_pw = 4.18 kJ/kg K

With this information, I found T₂ to be 304.6 K.

How can I obtain the entropy change with this information? I have no pressure values, and all my entropy equations involve pressure, or specific volume which depends on pressure. Thanks for any help.

 

[Mapes]

Do you know of an equation that connects dS to C_p that you might be able to integrate?

 

[mouser]

I did find a relationship, but it is returning negative values for me, so something is amiss...

s₂ - s₁ = C_p ln(T₂/T₁)

I'm trying to find the total entropy change. Would that mean that I sum the entropy change in the quenched metal and the water?

 

[stewartcs]

Would that mean that I sum the entropy change in the quenched metal and the water?

Yes.

CS

 

[Mapes]

Yes. It's not unusual for entropy to decrease; it happens whenever a hot object cools down.

 

[stewartcs]

I did find a relationship, but it is returning negative values for me, so something is amiss...

s₂ - s₁ = C_p ln(T₂/T₁)

You'll need to consider the mass of each as well in your equation.

CS

 

[stewartcs]

Yes. It's not unusual for entropy to decrease; it happens whenever a hot object cools down.

Caveat:

But the total change in the universe will always increase.

CS

 

[mouser]

Wow, thanks for all the responses everyone :). OK so here is what I came up with, and it seems to be giving me the right answer, but just for future reference:

s2-s1 = m_mC_pm ln(T₂/T_m1) + m_wC_pw ln(T₂/T_w1)