# Is it easier to gain energy or to lose it?

Here's an interesting question that came to my mind today:

Suppose I have two containers of water. I heat Container $A$ to $60°C$ and Container $B$ is chilled to $-20°C$. If I leave them both in rooms, which container of water will reach $20°C$ first (room temperature)? Assume every variable is controlled except the temperature of the water.

Container $A$ and Container $B$ are both $40°C$ from room temperature. Clearly Container $A$ needs to lose some thermal energy while Container $B$ needs to gain some. In both situations the water wants to reach thermal equilibrium at $20°C$, but which container will do it faster?

• and does container $B$ remain in the liquid state?
– Tofi
Commented Feb 19, 2018 at 11:40
• Actually the title and the body are totally unrelated. It is still possible to guess what are you asking for and as such you got answers and an important comment. Commented Feb 19, 2018 at 12:02
• Yes, assume both stay in the liquid state (perhaps water wasn't the best example). Commented Feb 19, 2018 at 12:06
• I still suggest that you change the title as" for a body or a system is faster to heat or to cool" , something like that. Commented Feb 19, 2018 at 12:40
• Isn't a point of view issue? Is one component of the system is gaining energy then another is losing it and vice versa. If you find that gaining is easier than losing then someone watching the rest of the system will get the opposite impression. Commented Apr 12, 2022 at 6:42

That depends on thermal capacity of the containers and thermal coductivity between the containers and the room. If the containers are exactly the same in these respects they will reach room temperature together.

• If conduction is the dominant form of heat transfer. This isn't the case if radiative heat transfer is significant.
– Chris
Commented Feb 19, 2018 at 10:56
• @Chris It's 2 containers of waters at less than 100°C, it's safe to assume that conduction is dominant. Commented Feb 19, 2018 at 12:49
• Also might want to make the more realistic caveat that the liquid at -20 is not frozen water since there will then be a heat of fusion required that is not required to cool the water at +60.
– hft
Commented May 20, 2022 at 0:42

There're two ways to interpret your question: based on the title, and based on the body of the question. I'll take the one based on the title, because it's simpler.

Generally speaking there is no difference between "gaining energy" and "losing energy" in this context. That's because if you examine the formula for conduction, it looks something like: $$q = -mk \nabla T$$, where $$q$$ is the heat flux density and $$\nabla T$$ is the temperature gradient. Note the formula depends on the temperature gradient, i.e. how fast the temperature is changing, but not on whether the heat flux is outwards or inwards (i.e. if the body is gaining energy or losing it). Whether the body gains energy or loses energy can be seen from the the sign, either negative or positive, but such a sign difference doesn't change the magnitude of the flux. So there is no difference.

The other interpretation of your question, based on the body, is significantly more complicated. That's because all sorts of minor effects can affect which body gains or loses energy faster. You would for example have to take into account radiation (which also does not depend on whether the body is gaining or losing energy, but does depend on what the ambient temperature is, and the latter can be different for the two containers). Someone else might model evaporative cooling, wherein some of the water in the hotter container evaporates and so there's less water in it, so it cools faster. And so on. There are tons of small effects that can all affect the result, making it more complicated.

I don't know.

The way I see the problem, the two containers of water conform the water to identical-shaped cylinders with the same surface area. In both, 40°C of energy must pass through this surface area. In this way, it looks symmetrical.

Airflow in the room - necessarily caused by temperature differences and gravity, would cause the air around the hot container to move upward and the air around the cold container downward but I don't see how that would matter, unless there was a difference in speed.

So, my guess is, it would be a tie - I don't know that but maybe my thought process could inspire a better answer!