Finding Specific Heat of a solid

[sarahjohn]

Homework Statement

For most solids at room temperature, the specific heat is determined by oscillations of the atom cores in the lattice (each oscillating lattice site contributes 3kT of energy, by equipartition), as well as a contribution from the mobile electrons (if it's a metal). At room temperature the latter contribution is typically much smaller than the former, so we will ignore it here. In other words, you can reasonably estimate the specific heat simply by counting the number of atoms!

Use this fact to estimate the specific heat of copper (atomic mass = 63.6), given that the specific heat of aluminum (atomic mass = 27.0) is 900 J/kg-K.

Relevant Equations

Q = mc(delta T)

I thought it might me a ratio of the atomic masses.
27 / 63.6 = x / 900
x = 382 J/kg-K

 

[Steve4Physics]

Hi @sarahjohn. In accordance with the rules here, you need to show that you have made some effort yourself before we can offer help. See Item 4 here: https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

Having said that, I will add that you should carefully read your homework statement. Does it suggest any possible approach?

 

[sarahjohn]

Hi @sarahjohn. In accordance with the rules here, you need to show that you have made some effort yourself before we can offer help. See Item 4 here: https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

Having said that, I will add that you should carefully read your homework statement. Does it suggest any possible approach?

Thank you for letting me know! I have updated my question.

 

[Steve4Physics]

Homework Statement:: For most solids at room temperature, the specific heat is determined by oscillations of the atom cores in the lattice (each oscillating lattice site contributes 3kT of energy, by equipartition), as well as a contribution from the mobile electrons (if it's a metal). At room temperature the latter contribution is typically much smaller than the former, so we will ignore it here. In other words, you can reasonably estimate the specific heat simply by counting the number of atoms!

Use this fact to estimate the specific heat of copper (atomic mass = 63.6), given that the specific heat of aluminum (atomic mass = 27.0) is 900 J/kg-K.
Relevant Equations:: Q = mc(delta T)

I thought it might me a ratio of the atomic masses.
27 / 63.6 = x / 900
x = 382 J/kg-K

Maybe! But is that a guess or is there some reasoning behind it? What is the reasonng?

 

[haruspex]

I thought it might me a ratio of the atomic masses.
27 / 63.6 = x / 900
x = 382 J/kg-K

Looks good.
From http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/sphtt.html

Substance	c in J/gm K	
Copper         0.386