Heat Capacity and KE

[MedPR]

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Confused about why something with higher heat capacity also has a higher amount of transferable kinetic energy.

Temperature is a measure of kinetic energy, right? And something with a lower heat capacity will have a more rapid increase in temperature compared to something with a higher heat capacity. So if Metal A has a lower heat capacity than metal B, metal A will get hotter than metal B when both are heated under the same conditions.

So if Metal A's final temperature is higher than Metal B's final temperature, doesn't Metal A have more heat (KE) to distribute than Metal B?

 

[davcro]

Good question. The phrase "transferable kinetic energy" is vague. What they mean is a metal with a large heat capacity can transfer more energy than a metal with a small heat capacity. For example Metal A has heat capacity of 10J / K and metal B is 1 J / K. When metal A is heated to 300K, it holds 3,000 Joules of energy. At the same temperature, metal B holds 300 Joules of energy. Drop both these metals into water and the one with the higher heat capacity will raise the temperature of the water more because it is storing 10 times the energy.

 

[MedPR]

Good question. The phrase "transferable kinetic energy" is vague. What they mean is a metal with a large heat capacity can transfer more energy than a metal with a small heat capacity. For example Metal A has heat capacity of 10J / K and metal B is 1 J / K. When metal A is heated to 300K, it holds 3,000 Joules of energy. At the same temperature, metal B holds 300 Joules of energy. Drop both these metals into water and the one with the higher heat capacity will raise the temperature of the water more because it is storing 10 times the energy.

Yea, that makes sense but that's assuming you heat both to the same temperature, rather than heating both for X amount of time and seeing which one gets hotter. Obviously the one with higher heat capacity will not get as hot.

The question was something like this.

Both metal A and metal B are heated under the same conditions. The starting temperature of both metals is 22 C. The final temperature of Metal A is 50 C and the final temp of Metal B is 100C.

Which metal has a higher heat capacity? Answer is metal A, since heat capacity is how much heat is required to change an object's temperature and not the ease heating or how hot an object can get.

Then it asked which metal had more kinetic energy. The answer was metal A.

I understand what you are saying, that if you heat both to 300K, the metal with the higher heat capacity will absorb more energy since it will need more energy to get to 300K.

But in a situation where two metals are heated under the same conditions (and thus not to the same final temperature due to varying heat capacity), why doesn't the hotter one have higher kinetic energy?

 

[davcro]

The hotter one should have a higher kinetic energy because has a higher temperature. But it has a lower transferable kinetic energy because it absorbed less heat.

I like to think of heat capacity as being similar to potential energy.

 

[MedPR]

The hotter one should have a higher kinetic energy because has a higher temperature. But it has a lower transferable kinetic energy because it absorbed less heat.

I like to think of heat capacity as being similar to potential energy.

Ah that makes sense. I didn't make that distinction. Thank you.

 

[fluoropHore]

can you elaborate on this "The hotter one should have a higher kinetic energy because has a higher temperature. But it has a lower transferable kinetic energy because it absorbed less heat." i get it on a superficial level.

 

[MedPR]

can you elaborate on this "The hotter one should have a higher kinetic energy because has a higher temperature. But it has a lower transferable kinetic energy because it absorbed less heat." i get it on a superficial level.

In a situation where you heat two things under the same conditions for a given amount of time, the hotter one is easier to heat (has lower heat capacity), so it absorbs less energy to get to its current temperature. The less hot one requires more energy to heat, since it has a higher heat capacity.

So even though the hotter one has molecules with higher kinetic energy, it has not abosrbed as much heat energy as the colder one has. Since it hasn't absorbed as much energy, it can't give off as much energy.

 

[fluoropHore]

ah perfect, thanks!