5.2 Specific Heat
Now we can introduced the concept of heat change and transfer measurements. The heat capacity C of a matter is defined as the heat (energy) q absorbed or released when this matter is exposed to a temperature change ∆T of 1 oC or 1 K (Kelvin).
C = q / ∆T
Heat capacity C is an extensive property of the matter, which means it depends on the amount of the matter.
For example: The heat capacity of 250.0 grams of Iron metal is 10 times higher than the heat capacity of 25.0 grams of the same of Iron.
We expand the formula further by looking at concept of the specific heat and the molar heat capacity of a matter which is defined as follows:
Specific Heat:
c = q / m ∆T and q = m c ∆T
Where:
c = specific heat
q = heat
∆T = temperature change
m = mass of the matter
The specific heat c is defined as the amount of energy needed to raise the temperature of 1.0 gram of a matter 1.0 degree (1.0 oC or 1 K). The unit of the specific heat is cal / g x oC or 4.184 J / g x oC.
The specific heat is an intensive property of the matter which means it does not depend on the amount of the matter.
Example: the specific heat of 100.0 grams aluminum metal is equal to the specific heat of 10.0 grams of the same aluminum metal which is in both cases 0.2156 cal / g x oC or 0.902 J / g x oC
Example of the Specific Heats for some substances is given below:
Reference: file:///C:/Users/matteya/Downloads/Metal%20HeatLAB.pdf
Molar Heat Capacity:
From its name “molar”, one will think that the mole of matter is involved. This is true and molar heat capacity is defined as:
Cn = q / n ∆T and q = n cn ∆T
Where:
Cn = molar heat capacity
q = heat
∆T = temperature change
n = number of moles of the matter
The molar heat capacity cn is defined as the amount of energy needed to raise the temperature of 1.0 mole of a matter 1.0 degree (1.0 oC or 1 K). The unit of the molar heat is cal / mole x oC or 4.184 J / mole x oC.
The molar heat is an intensive property of the matter which means it does not depend on the amount of the matter.
Example: the molar heat of 100.0 moles aluminum metal is equal to the molar heat of 10.0 moles of the same aluminum metal which is in both cases 5.808 cal / mole x oC or 24.3 J / mole x oC
The videos below explain the terms of heat capacity, the specific heat of capacity and the molar heat capacity:
What Is The Difference Between Specific Heat Capacity, Heat Capacity, and Molar Heat Capacity
Heat Capacity, Specific Heat Capacity and Molar Heat Capacity
Heat Calculations Examples
- How much heat in kilojoules has to be removed from 250.0 g of water to lower its temperature from 55.0 oC to 25.0 oC?
c = q / m ∆T
c = specific heat of water = 1 cal /g x oC = 4.184 J / g x oC
q = m c ∆T = [250.0 g x 4.184 J /g x oC] x [55.0 – 25.0] oC = 31380 J = 31.380 kJ = 31.4 kJ
- Calculate the mass of water that gives heat of 585.0 kilojoules when its temperature is decreased from 83.50 oC to 13.50 oC?
c = q / m ∆T
m = q/ c ∆T
c = specific heat of water = 1 cal /g x oC = 4.184 J / g x oC
m = [585.0 x 103 J] / [4.184 J /g x oC] x [70.00 oC] = 1997 g
- 25.0 g of mercury is heated from 25°C to 155°C, and absorbs 455 Joules of heat in the process. Calculate the specific heat capacity of mercury
c = q / m ∆T
c = [455 J] / [25.0 g] x[155 – 25] oC = 0.14 J / g x oC
- What is the specific heat capacity of silver metal if 55.00 g of the metal absorbs 47.3 calories of heat and the temperature rises 15.0°C?
c = q / m ∆T
c = [47.3 cal] / [55.00 g] x [15.0 oC] = 0.0573 cal / g x oC
- If a sample of chloroform is initially at 25.0 °C, what is its final temperature if 150.0 g of chloroform absorbs 1.00 kilojoules of heat, and the specific heat of chloroform is 0.960 J / g x °C?
c = q / m ∆T
∆T = q / m x c
∆T = [1.00 x 103 J] / [150.0 g] x [0.960 J / g x °C] = 6.944 °C
∆T = T(final) – T(initial) = 6.044 °C = T(final) – 25.0 °C = 31.9 °C
The video below goes over some examples:
How to calculate specific heat: Example specific heat problems