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# How to Calculate and Solve for Volumetric Heat Capacity of Metal | Energy Transport

Last Updated on September 24, 2021

The image above represents volumetric heat capacity of metal.

To compute for volumetric heat capacity of metal, four essential parameters are needed and these parameters are Fermi Energy (εf), Number of Free Electrons (ne), Temperature (T) and Boltzmann’s Constant (KB).

The formula for calculating volumetric heat capacity of metal:

cvol = π²neKB²T / 2εf

Where:

cvol = Volumetric Heat Capacity of Metal
εf = Fermi Energy
ne = Number of Free Electrons
T = Temperature
KB = Boltzmann’s Constant

Let’s solve an example;
Find the volumetric heat capacity of metal when the fermi energy is 4, the number of free electrons is 2, the temperature is 5 and the boltzmann’s constant is 1.38E-23.

This implies that;

εf = Fermi Energy = 4
ne = Number of Free Electrons = 2
T = Temperature = 5
KB = Boltzmann’s Constant = 1.38E-23

cvol = π²neKB²T / 2εf
cvol = π²(2)(1.380e-23)²(5) / 2(4)
cvol = (9.869)(2)(1.90e-46)(5) / 8
cvol = 1.88e-44 / 8
cvol = 2.35e-45

Therefore, the volumetric heat capacity of metal is 2.35e-45 J/K.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the volumetric heat capacity of metal.

To get the answer and workings of the volumetric heat capacity of metal using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

You can also try the demo version via https://www.nickzom.org/calculator

Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.

Now, Click on Energy Transport under Materials and Metallurgical

Now, Click on Volumetric Heat Capacity of Metal under Energy Transport

The screenshot below displays the page or activity to enter your values, to get the answer for the volumetric heat capacity of metal according to the respective parameter which is the Fermi Energy (εf), Number of Free Electrons (ne), Temperature (T) and Boltzmann’s Constant (KB).

Now, enter the values appropriately and accordingly for the parameters as required by the Fermi Energy (εf) is 4, Number of Free Electrons (ne) is 2, Temperature (T) is 5 and Boltzmann’s Constant (KB) is 1.38E-23.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the volumetric heat capacity of metal and presents the formula, workings and steps too.