# Why does a heavier element have a low specific heat capacity?

Lead has 207 amu and 125j/kg/c while copper has 63 amu and 376 j/kg/c, why is that? So if energy is stored in the motion of the particles, heavier particles should move slower and therefore wouldn't this means that it require more energy to increase the temperature by 1-degree Celcius? I looked up on google and the main reason it said is that there are more particles, but how? I am taking 1 kg of lead and 1 kg of copper, and from my understanding, their masses are different because the lead particles are heavier instead of more of particles in lead than copper. So please explain why does a heavier element tend to have a low specific heat capacity?

I think you mean to say that they have a different number of particles- 1kg of lead and 1kg of copper surely have the same mass.

There are $$~2.91\times10^{24}$$ atoms in a kg of lead, and $$~9.45\times10^{24}$$ atoms in a kg of copper. Heat (more accurately, thermal energy) is "stored" in the particular degrees of freedom for the motion of the atomic "particles"- and since there are more atoms in a kilogram of copper, it's gonna have more atoms with more degrees of freedom. Thus, more capacity for storage.

• how are there more atoms in a 1 kg of copper? And how do calculate how many atoms there are? – Fred Weasley Apr 19 at 5:21
• You can find the number of particles in a given mass of a pure substance using the substance's atomic mass, the given mass, and avogadro's number. Taking 1kg of copper for example, copper has an atomic mass of ~63.5 amu( units of grams/mol). Dividing 1kg by 63.5 gives ~15.7 moles of copper- and multiplying this number by Avogadro's number tells you the number of particles in in the given quantity of substance. – swickrotation Apr 20 at 2:02

Lead has 207 amu and 125j/kg/c while copper has 63 amu and 376 j/kg/c, why is that?

Because lead has a higher atomic mass, but that isn't a very complete answer.

So if energy is stored in the motion of the particles, heavier particles should move slower and therefore wouldn't this means that it require more energy to increase the temperature by 1-degree Celcius?

No. Temperature is a measure of the average kinetic energy, not the average velocity.

Okay but still why a difference? You have to consider that copper has a lower standard atomic weight thus for 1kg of copper the amount of substance is more than the for 1kg of lead (i.e. 3 times more atoms in 1kg of copper than 1kg of lead). Think: a pound of bricks and a pound of feathers have the same mass, but it takes many more feather feathers than bricks to make that one pound.

Temperature is the average kinetic energy on a per atom/particle basis. For any given atom/particle with a given energy the temperature can be calculated. If a particle has more energy, it has a higher temperature, if you have two particles that weight half as much and have half as much energy as the initial particle then even though in aggregate they have the same mass and energy, the total energy is the same, but the average energy is half thus the temperature is lower.

If you look at metals on a atomic basis you will find that the molar specific heat of metals can be approximated by the Dulong-Petit Law to be: $$C_v \approx 3R$$ where $$R$$ is the ideal gas constant and $$C_v$$ is a molar heat capacity. Again this is an approximation, but the values are much close as copper has a $$C_v$$ of $$24.6~\mathrm{J~mol^{-1}~K^{-1}}$$ and lead has a $$C_v$$ of $$26.5~\mathrm{J~mol^{-1}~K^{-1}}$$.

If you want to approximate a specific heat capacity based on weight just divide $$3R$$ by the standard atomic weight ($$A_r$$):

$$C_v(\text{mass}) = \frac{3R}{A_r}$$

• how are there more atoms in a 1 kg of copper? And how do calculate how many atoms there are? – Fred Weasley Apr 19 at 5:23
• and also i want specific heat capacity not molar specific heat. – Fred Weasley Apr 19 at 11:15
• @FredWeasley Because lead has a higher standard atomic weight than copper thus it takes more copper atoms to have 1kg of copper than for 1kg of lead. Think: a pound of brick and a pound of feathers weight the same, but it takes many more feathers than bricks to make that pound – A.K. Apr 19 at 16:33
• @FredWeasley edited. – A.K. Apr 19 at 16:59