# Moving heat from mercury to water; raise water temp by X to lower mercury temp by 1°

If I have equivalent amounts of mercury and water, and transfer heat from the mercury to the water, how much do I have to raise the temperature of the water to lower the temperature of the mercury by one degree?

Is there some sort of term or number that makes this easy to figure out?

Thanks much.

If you know the specific heat (c) of mercury - the amount of heat required to raise one gram of the substance by one degree Celsius/Kelvin - you can set up a parallel equation as follows:

q[sub]Hg[/sub] = m[sub]Hg[/sub] x c[sub]Hg[/sub] x ΔT[sub]Hg[/sub]
q[sub]H2O[/sub] = m[sub]H2O[/sub] x c[sub]H2O[/sub] x ΔT[sub]H2O[/sub]

Since the amount of energy (q) required should be the same, ΔT[sub]Hg[/sub] = 1 degree (same amount of change in Celsius or Kelvin, if you were thinking about Fahrenheit you just need to convert) and c[sub]H2O[/sub] = 4.184 kJ g[sup]-1[/sup] K[sup]-1[/sup], you should be able to rearrange the equation to be:
ΔT[sub]H2O[/sub] = m[sub]Hg[/sub] x c[sub]Hg[/sub] x 1 / m[sub]H2O[/sub] / 4.184

That should tell you the change in temperature of the water required to lower the amount of mercury by one degree Celsius/Kelvin. Sorry if the formatting of the equation is confusing, but I haven’t yet worked out how to legibly put mathematical equations into vB code

The important number here is called heat capcity or specific heat, and is normally given in Joules per degree C per gram. For water, this value is 4.18; for mercury it is given as .14. Thus, to raise a given quantity of water by 1 degree C, you must transfer enough heat energy to lower the temperature of an equal amount of mercury by almost 30 degrees (29.9).

The term is specific heat.

The specific heat of mercury is 0.14. The specific heat of water is 4.179.

So, if one gram of mercury loses 1 degree of temperature, it would increase the temperature of the one gram of water 0.14/4.179 or 0.03 degrees.

Now, since I did that while talking on the phone, I’m sure I screwed it up.

Sure, you guys do it the easy way …

Opps, I had it backwards. You wanted the temperature change of the water, not the mercury. So, take the inverse of 29.9, which is .033; this is in agreement with previous posters.

I wonder why this question is posted asking about “equivalent amounts”? There could be any numbe rof answers depending on what that means. Most of the asnwers below have assumed you meant equal masses.

If you meant equal volumes, then of course you could do it the same way and would have to convert based on the densities. I don’t have the density of Hg available right here, but it’s a lot higher tha water, so it’s going to take a much larger change in the temperature of the water to affect the temperature of the same volume of Hg.

Of course equivalent could also mean the same number of molecules or even the same specific heat content. In the latter case the answer is easy. It’s one for one by definition. So if someone asks you a carelessly worded question always go for the easy way out

Because it is hard to ask questions when one knows nothing about what one is asking. It’s actually for my NaNo novel, so I’m glad you pointed that out.

A Most Profound Statement!

Another OP to justify our existence.