Heat Capacity Formula

Heat is a form of energy that travels from objects with higher temperatures to those with lower temperatures. The heat energy from our bodies transfers to a glass of cold water when we touch it. This is better explained by heat capacity. The amount of heat energy that a substance can absorb or release when its temperature changes is known as its heat capacity. Heat Capacity Formula is used to measure the heat capacity.

Students can learn about heat capacity, the formula to calculate heat capacity and other related concepts in depth in this post by Extramarks.

Heat Capacity

Heat capacity is a thermodynamic property of substance that indicates the quantity of heat required to change a substance’s temperature by a specific amount.

It is a measure of how much heat energy a substance can absorb or release when its temperature changes.

• Even objects with separate parts made of different materials, like an electric motor, a crucible with some metal, or an entire structure, can have well-defined heat capacities.
• The heat capacity of such objects is frequently calculated by merely adding the heat capacities of the component parts.
• This calculation, however, is only accurate if the object’s entire surface is under the same external pressure both before and after the measurement.

Heat capacity is measured in units like joules per degree Celsius (J/°C)

Heat Capacity and Second Law of Thermodynamics

Second Law of Thermodynamics states that heat will flow from a hotter system to a cooler system when two systems with different temperatures interact through a purely thermal connection.

• These systems are at thermal equilibrium if their temperatures are equal.
• However, the systems must have positive heat capacities in order for this equilibrium to be stable.
• For such systems, when heat moves from a system with a higher temperature to one with a lower temperature, the temperature of the former falls and the latter rises, bringing both systems closer to equilibrium. 

Formula of Heat Capacity

Heat capacity (C) of a substance is defined as the amount of heat energy (Q) required to raise the temperature (ΔT) of the substance by one degree Celsius. The formula of Heat Capacity is given as

C = Q/ΔT

where,

• C is Heat Capacity
• Q is Heat Transferred
• ΔT is Temperature Difference

In the above formula the amount of heat transferred is given by the following formula

Q = m x Cs x ΔT

here,

• Q is Heat
• m is mass of the substance
• Cs is Specfic Heat of the substance
• ΔT is Temperature Difference

Specific Heat Capacity

Specific heat capacity, sometimes expressed simply as specific heat, is defined as the amount of heat energy that should be added to a unit mass of a given substance to increase its temperature by one degree Celsius. Different substances display varying specific heat capacities. Therefore, it takes different amounts of heat to heat or cool them to the required temperature brought about by the change. The formula of specific heat capacity is given as

Cs = Q/(m x ΔT )

where, symbols have usual meaning as above.

The unit of specific heat capacity is J/°C/kg

Molar Heat Capacity

Molar Heat capacity calculates the amount of heat energy needed to increase a substance’s temperature by one degree Celsius (or Kelvin) per mole.

The formula for molar heat capacity is given as

Cm = Q/(n x ΔT )

where,

• Cm is Molar Heat Capacity
• Q is heat absorbed
• n is number of moles
• ΔT is temperature difference

The unit of Molar Heat capacity is J/°C/mol

Difference between Heat Capacity and Specific Heat Capacity

The difference between heat capacity and specific heat capacity is given below

Heat capacity is a measure of the total amount of heat energy needed to raise the temperature of a substance by a certain amount while specific heat, is a measure of the amount of heat energy required to raise the temperature of a unit mass of a substance by a certain amount.

Heat capacity depends on mass of substance while specififc heat capacity does not depend on mass of substance

The unit of heat capacity is J/K while the unit of specific heat capacity is J/(K.Kg)

Solved Examples on Heat Capacity

Example 1

A matter with a mass of 250 grams absorbs 1500 joules of heat energy. If its temperature increases by 20°C, what is the heat capacity of the matter?

Solution

Given:
Q = 1500 J
ΔT=20°C
m=250g

We can use the formula for heat capacity:

C=Q/ΔT

C=1500J/20°C

Therefore, C=75J/°C