Heat Capacity Formula

Heat Capacity Formula:

Heat capacity is defined as the heat required to increase an object temperature by one degree.

The heat capacity of an object is expressed in joules or calories and temperature in Kelvin or Celsius. Heat gain or heat loss results in change of temperature, state, and performance of the work. 

Heat Capacity depends on the initial temperature and the final temperature.

Heat capacity, Q = mc Δ T

Where,

• Q is the  heat capacity
• m is the mass
• c is the specific heat of an object.
• ΔT is the change in temperature.

Heat Capacity is the amount of energy that is required to raise the temperature of a specific object by 1 degree Celsius. The heat capacity unit is joules per kelvin (J/K). Every object in the earth has a different heat capacity. Heat capacity is the internal property of an object. Water has a heat capacity of 4184 J/kg.

Heat Capacity does not depend on the substance quantity. Heat capacity is transformed from a higher temperature body to a lower temperature body.

Solved examples:

1) A 125-g piece of iron (specific heat is equal to 0.45 J/gºC) is heated from 100 º C to 450º C. How much heat energy is required?

The mass, m = 125 g; the specific heat of iron, c = 0.45 J/gº C, and the change in temperature, ΔT = 350 º C.

Q = mc Δ T

Q = (125) (0.45) (350)

Q = 19687.5 J

2) If 15, 250 J of heat are applied to a copper ball with a mass of 40 g, how much will the temperature change? Specific heat of copper is equal to 0.40 J/gº C.

The mass, m = 40 g; the specific heat, c = 0.40 J/gº C; and Q = 15250 J.

Q = mc Δ T

Q / mc= Δ T

(15250 ) / (40 )(0.40) = Δ T

ΔT = 953.125 º C

3) Determine the heat capacity of copper of mass 70 g and the temperature difference is 10oC if 200 J of heat is lost.

Given that Mass m = 70 g,

Temperature difference T = 10oC,

Heat lost Δ Q = 200 J

Heat capacity formula is Q = mc ΔT

c= 200 / 10

c = 20J /°C