Specific Heat Capacity

by Dejan Tojcic

Specific Heat Capacity

Specific Heat Capacity is simply a physical quantity that represents the ratio of the amount of heat taken or added to substance or object which results in a temperature change. The formal definition of Specific Heat is the amount of heat required to raise the temperature of 1 gram of a substance 1°C. The Standard Unit(SI) of this quantity is, joule per celsius per kilogram or or [math]\displaystyle{ \mathrm{\tfrac{J}{°C*Kg}} }[/math]. Different objects/substances have different specific heat capacities because every object has a varying mass, molecular structure, and numbers of particles per unit mass specific, and since specific heat capacity is reliant on mass, every different object has a different specific heat capacity.

A Mathematical Model

In order to find the Specific Heat Capacity of a substance, we use the equation:[math]\displaystyle{ \Delta E_{\mathrm{thermal}} = C * M * \Delta T }[/math], and rearrange it to get [math]\displaystyle{ C= \Delta E_{\mathrm{thermal}} /( M * \Delta T) . }[/math] where C is the Specific Heat Capacity with units of joules per celsius per kilogram or [math]\displaystyle{ \mathrm{\tfrac{J}{°C*Kg}} }[/math], M is the mass measured in kilograms or [math]\displaystyle{ \mathrm{kg} }[/math], [math]\displaystyle{ \Delta E_{\mathrm{thermal}} }[/math] represents the change in thermal energy measured by joules or [math]\displaystyle{ \mathrm{J} }[/math], and [math]\displaystyle{ \Delta T }[/math] represents change in temperature with units celsius or [math]\displaystyle{ \mathrm{°C.} }[/math]

A Computational Model

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Simple Example

Question 
It takes 487.5 J to heat 25 grams of copper from 25 °C to 75 °C. What is the specific heat in Joules/g·°C?

In this example, the electric field is equal to [math]\displaystyle{ E = \left(E_x, 0, 0\right) }[/math]. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use [math]\displaystyle{ dV = V_C - V_A }[/math].

Since there are no y and z components of the electric field, the potential difference is [math]\displaystyle{ dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right) = -E_x*x_1 }[/math]

Let's say there is a location B at [math]\displaystyle{ \left(x_1, 0, 0\right) }[/math]. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C.

The potential difference between A and B is [math]\displaystyle{ dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1 }[/math].

The potential difference between B and C is [math]\displaystyle{ dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0 }[/math].

Therefore, the potential difference A and C is [math]\displaystyle{ V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 }[/math], which is the same answer that we got when we did not use location B.

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