ek 1001 entropy question

[deleted388502]

Two large heat reservoirs are connected by a thin metal bar. The first heat reservoir is 300K. The second heat reservoir is 100K.

As heat is transferred through the bar from the hot reservoir to the cooler one, which reservoir experiences the greatest change in entropy?
A. The cold reservoir because the same amount of energy change has a greater proportional effect
B. The hot reservoir because it is losing energy
C. There is no change in entropy because the system is isolated
D. Since the same amount of energy leaving one enters the other, they both experience the same change in entropy

EK says A because "since this is a spontaneous process that does not exchange heat with the environment, the total entropy of the system must increase. Therefore, the gain in entropy by the cold reservoir must be larger than the loss in entropy by the hot reservoir."



Can anyone clarify?

Thanks!

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[Czarcasm]

Two large heat reservoirs are connected by a thin metal bar. The first heat reservoir is 300K. The second heat reservoir is 100K.

As heat is transferred through the bar from the hot reservoir to the cooler one, which reservoir experiences the greatest change in entropy?
A. The cold reservoir because the same amount of energy change has a greater proportional effect
B. The hot reservoir because it is losing energy
C. There is no change in entropy because the system is isolated
D. Since the same amount of energy leaving one enters the other, they both experience the same change in entropy

EK says A because "since this is a spontaneous process that does not exchange heat with the environment, the total entropy of the system must increase. Therefore, the gain in entropy by the cold reservoir must be larger than the loss in entropy by the hot reservoir."



Can anyone clarify?

Thanks!

I guess a better analogy worth considering is phase changes. To go from liquid to liquid-gas equilibrium would require heat input (causes increased vibration of the molecules). To go from gas to liquid-gas equilibrium would require heat release (the molecules are vibrating less). Both are in liquid-gas equilibrium, so they're at the same temperature. However, relative to each other, increasing the temperature of water was an overall increase an entropy compared to the cooling of gas. Similarly here, both have the same temperature at thermal equilibrium. For this to happen, the hotter reservoir loses heat (-q). The cooler reservoir gains heat (+q). Such that together, their sum = zero. And if it helps, an equation sometimes given for entropy is: deltaS= deltaQ/T (Here, T is the same, but deltaQ - although the same magnitude, is very different in sign).

 

[techfan]

Something that was beaten into my head in all of the physics/thermo classes I've taken is that entropy is always increasing and that things always want to become more disordered (common "hilarious" physics prof joke was "Tell your mom that by cleaning your room you are contributing to the heat death of the universe").

Entropy is a tricky subject for most people (reason why statistical mechanics is one of the toughest courses offered in undergrad), and the MCAT is only really going to test to see if you know that disorder is favored over order thermodynamically (at least on a conceptual level).