Heat Formula

Thermal physics deals with many equations and formulas that are found useful in every aspect of science. One of the useful formulas in the field of thermal physics is the heat formula. We know that heat is another form of energy that is transferred between two substances maintained at different temperatures. The direction of the flow of energy is always from the substance maintained at a higher temperature to the substance kept at a lower temperature. The heat energy also transmits from hotter bodies to the lower bodies without violating the law of conservation of energy.

Heat is usually measured in terms of energy, thus the unit of heat is the same as the unit of energy i.e. calories or joules. students often get confused with the terms heat and temperature, heat is the effect of temperature and they are not the same. Heat and temperature can not be interchanged, but this is incorrect. Heat and temperature can not be interchanged because the temperature will measure the level of hotness or coldness of material under observation. In this article, we will discuss the heat formula, specific heat formula, specific heat capacity formula, enthalpy formula with solved numerical problems. 

Specific Heat Formula:

We know that the term specific heat in thermodynamics refers to the ratio of the quantity of heat that we require to raise the temperature of a substance by one-degree celsius that we need to increase the temperature of an equivalent mass of liquid (say water) by one-degree celsius. At the same time, we use the term specific heat for a more conventional reason to determine the amount of heat in calories that we require to raise the temperature of one gram of a material by one degree Celsius degree.

In simple words, the specific heat equation or the specific heat formula is the ratio of the amount of heat required to raise the temperature of a substance by one degree Celsius to the amount of heat required to raise the temperature of the equal amount of water by one-degree Celsius at room temperature.

The term Specific heat is generally used when we are referring to something particular, such as we are referring to raising the temperature of a particular substance. Now, usually, everyone gets confused between the specific heat and the heat capacity. 

Specific Heat Capacity Formula:

The heat capacity is the ratio of the quantity of heat required to alter the temperature by one degree Celsius, whereas the specific heat is the amount of heat required to raise the temperature of the substance, not just to change or alter the temperature of the material. One important point to note down here is that when we consider a particular amount of mass we tend to use the word Specific Heat or Specific Heat Capacity.  The specific heat capacity of most of the thermodynamic systems is not constant and it depends on physical entities such as pressure, volume and temperature.

Derivation:

Now, let us have a look at the specific heat formula or specific heat capacity formula, which is denoted by the letter C. According to the definition of the specific heat, we have seen that it is directly proportional to the temperature change (in particular raising temperature). We know that amount of heat required (Q) is directly proportional to the change in temperature, thus we write:

⇒ Q ∝ ΔT ……(1)

Where,

ΔT - The change or raise in the temperature

Also, we know that the specific heat is also directly proportional to the mass of the substance under consideration, thus we get:

⇒ Q ∝ m ……..(2)

Where,

m - The mass of the substance

Combining equation (1) and (2) we get:

⇒ Q ∝ mΔT

⇒ Q = CmΔT

Where,

C - The specific heat 

Thus, the specific heat equation is given by:

⇒ C = \[\frac{Q}{m \Delta T }\]

Or

⇒ C = \[\frac{\Delta Q}{m \Delta T }\] joules/kg\[^{0}\]c……..(3)

Where,

\[\Delta\]Q - The amount of heat gained or lost in joules

\[\Delta\]T - The change or raise in the temperature in degree celsius

m - The mass of the substance in kg 

Equation (3) is known as the specific heat capacity formula or specific heat formula in physics and it is used to solve specific heat examples and to estimate specific heat of substance in real life. The specific heat substance will vary depending on the type of substance.

Latent Heat Formula:

Just like the specific heat capacity formula, many more thermal formulas can be derived such as latent heat formula, thermal conductivity formula, heat transfer formula, and heat energy formula etc., which can be used for the calculation of various parameters of the given thermodynamic system.

One of the useful formulas in thermodynamics is the latent heat capacity or latent heat formula. Latent heat can be defined as the amount of heat absorbed or released by a thermodynamic system for phase change at a constant temperature. Or in other words, Latent heat is the amount of heat required to convert phases of material i.e., a solid into a liquid or vapour phase, or a liquid into a vapour phase or vice versa. Depending on the phase conversion latent heat is having different tags. Latent heat is also known as the heat of condensation, the heat of vaporization, etc. 

It is also defined as the ratio of the amount of heat absorbed or released to the mass of the substance. It is denoted by the letter L and the latent heat formula is given by:

⇒ L = \[\frac{Q}{m}\]

Where,

Q - The amount of heat supplied

m - The mass of the substance

The latent heat of a substance is measured in units of Cal/ g. The examples of latent heat are latent heat of vaporization of latent heat of condensation, where the substance either absorbs and evaporates or condenses to form a precipitate.

Examples:

1. Calculate the Amount of Heat Required to Raise 4kg of Water From 30⁰c to 70⁰c? (specific Heat of Water = 4.2 x 10³ j/kg⁰c)

Sol:

Given,

The mass of the water = m = 6kg

The change in temperature = ∆T = T₂ - T₁ = 70 - 30 = 40⁰c  

The specific heat capacity of the water = C = 4.2 x 10³ j/kg⁰c

Now, we aim to determine the amount of heat required to raise the temperature of 6kgof water from 40⁰c to 80⁰c. Thus, we know that the amount required is given by the equation:

⇒ Q = Cm∆T

Where,

C - The specific heat of the substance

∆T - The change or raise in the temperature

m - The mass of the substance

Substituting, required values in the above expression:

⇒ Q = Cm∆T = (4.2 x 10³)(4)(40)

⇒ Q = 672 x 10³ joules

⇒ Q = 672 kj

Therefore, the amount of heat required to raise 4kg of water from 30⁰c to 70⁰c is 672 kj.

2. Estimate the Latent Heat of 4kg Substance if the Amount of Heat Required for a Phase Change Is 300 K Cal.

Sol:

Given,

The mass of the substance = m = 4kg

The amount of heat required for a phase change = Q = 300 k cal

We are asked to determine the latent heat of the substance. We know that the latent heat formula is given by the equation:

⇒ L = \[\frac{Q}{m}\]……..(1)

Where,

Q - The amount of heat supplied

m - The mass of the substance

Substituting given values of the Q and min the equation (1) we get:

⇒ L = \[\frac{Q}{m}\] = \[\frac{300 \times 10^{3}}{4 \times 10^{3}}\] = 75 cal / g

Therefore, the latent heat of the substance is 75 cal/ g.