Entropy Change in a System with a Man Drinking Water

[scharry03]

Homework Statement

Man with a temperature of 310.15 K and a mass of 70 kg drinks 0.4536 kg of water at 275 K. Ignoring the temperature change of the man from the water intake (assume human body is a reservoir always at same temperature), find entropy increase of entire system.

Homework Equations

dS = - absvalue(Q)/Tbody
deltaS = mcln(Tfinal/Tinitial)

The Attempt at a Solution

I'd tried solving only using the second equation on here, but the answer only used that equation for the deltaS of the water. The natural log of the body would be 0, since T is constant, so I thought there wouldn't be an enthalpy change for the body. I don't understand under what circumstances the first equation would be used instead of the second equation. Also, the numbers plugged into the first equation for the deltaS(body) are -m(water)(1) [(Tbody-Twater)/Tbody] which is nothing like what the first equation asks for, so I am very confused.

 

[scharry03]

Homework Statement

Man with a temperature of 310.15 K and a mass of 70 kg drinks 0.4536 kg of water at 275 K. Ignoring the temperature change of the man from the water intake (assume human body is a reservoir always at same temperature), find entropy increase of entire system.

Homework Equations

dS = - absvalue(Q)/Tbody
deltaS = mcln(Tfinal/Tinitial)

The Attempt at a Solution

I'd tried solving only using the second equation on here, but the answer only used that equation for the deltaS of the water. The natural log of the body would be 0, since T is constant, so I thought there wouldn't be an enthalpy change for the body. I don't understand under what circumstances the first equation would be used instead of the second equation. Also, the numbers plugged into the first equation for the deltaS(body) are -m(water)(1) [(Tbody-Twater)/Tbody] which is nothing like what the first equation asks for, so I am very confused.

Does it mean another way to find deltaS(hot) is to do m(cold) x c(cold) x [(T(hot)-T(cold)/Thot] ?

 

[Chestermiller]

For the case of the constant temperature reservoir, this is a limiting case taken in the limit as its mass times its heat capacity becomes very large. So the second equation does actually apply to this situation, but only in the limit. Try doing the problem again, but instead, treat the reservoir as having a finite product of mass times heat capacity. What is the equation for the final temperature in this situation? Based on this result, what is the equation for the change in entropy of the water, the reservoir, and the total? Now, take the limit of the equations as the mass times the heat capacity of the reservoir becomes very large. See what you get.

Chet

 

[scharry03]

I've never framed these questions in terms of limits as you are doing, so I don't really understand what you mean. I had a chance to ask my professor about this and he said the first equation is used in something whose temperature isn't changing, and the second is used in the case that it is. How would you rephrase this in terms of limits, so that I can understand that method of thinking?

 

[Chestermiller]

I've never framed these questions in terms of limits as you are doing, so I don't really understand what you mean. I had a chance to ask my professor about this and he said the first equation is used in something whose temperature isn't changing, and the second is used in the case that it is. How would you rephrase this in terms of limits, so that I can understand that method of thinking?

I can help you with this if you are willing to work with me. Instead of ignoring the temperature change of the man, we will include it.

Let:

M_m=mass of man
C_m=heat capacity of man
M_w= mass of water
C_w=heat capacity of water
T_h=starting temperature of man (e.g., 310)
T_w=starting temperature of water (e.g., 275)
T = final equilibrated temperature of man and water

From a heat balance (algegraically), what is T in terms of the other parameters?
How much heat is transferred from the man to the water to achieve this temperature change?
Using the second equation, what is the entropy change of the man (algebraically)?
Using the second equation, what is the entropy change of the water (algebraically)?

Let's stop here and see what you come up with. Then we can take the limits as M_m becomes large.

Chet