**Thermal Energy: Concept and Equation**

It is the energy contained within a system that results in the existing temperature of the system. The total energy of a system is the summation of its thermal energy and kinetic energy. This phenomenon also leads to the conservation of Energy. Heat is nothing but the flow of Thermal Energy.

Heat is produced with the movement of particles within an object. Hence, the faster the movement the more heat gets generated. In Physics, the branch of Thermodynamics exclusively deals with the transfer of heat between different systems.

- In general, the specific heat capacity is the energy required to raise the temperature, per kilogram of material, per degree of temperature increase. Specific Heat Capacity is calculated as:

Thermal energy input divided by (mass) × (temperature change)

- In the absence of Specific heat to calculate the thermal energy, the heat transferred can be calculated instead. The formula used is as follows:

**Heat transferred = mass x specific heat capacity x (final temperature – initial temperature)**

- The Thermal energy of any substance is expressed using the symbol
**Q**. This is directly proportional to the mass of the substance, temperature difference and the ascertained heat of the object at a specific point of time.

The SI unit used to represent Thermal energy is Joules(J).

A system’s Thermal Energy is represented by using the following equation:-

**Equation key:**

Where

* Q* = thermal energy

* M* = mass of the given substance

* C* = specific heat

* ΔT* = temperature difference.

**Solved Questions**

Q) Find the thermal energy of a substance whose mass is 5 kg and specific heat is 0.030 J/ kg°c. We measure the temperature difference of the system as 30°c.

**Answer:**

M = 5 kg,

C = 0.030J/kg°c,

ΔT = 30°c

We calculate thermal energy formula as,

Q = mcΔT

\= 5 × 0.030 × 30

Hence, Q = 4.5 J

Q) What measurement of energy can increase the temperature of 200 grams of copper by 20 ºC. In the absence of the initial and final temperatures, the if the specific heat of the copper is 386 J/kgºC ?

**Answer:** Since we do not have an initial or final temperature specified in the question for the measurement of copper, so the calculation of the heat transferred is used by temperature difference between the two stages. This is shown using the following equation:-

**Heat transferred = mass x specific heat capacity x (final temperature – initial temperature)**

Tf-Ti = 20 ºC, m = 200 g = 0.2 kg, CP = 386 J/kgºC.

Q = m x CP(Tf-Ti) Q = 0.2 kg* 368 J/kgºC* 20 ºC Hence, Q = 1472 J.

Q) A substance weighing 9 kg undergoes an exponential temperature shift of 60 °C whose specific heat measurement when noted is 0.07 J/kg °C. Calculate the thermal energy of the object.

**Answer:**

M = 9 kg,

C = 0.07J/kg °C,

ΔT = 90 °C

We calculate the thermal energy formula as,

Q = mcΔT

\= 9×0.07×90

Hence, Q = 56.7 J

Q) Find the thermal energy of a piece of wood whose aggregate mass is 10 kg and the specific heat is gauged at 0.030 J/kg°c. The temperature difference of the system is measured as 30°c.

**Answer:**

M = 10 kg,

C = 0.030J/kg°c,

ΔT = 30°c

The thermal energy formula is calculated as,

Q = mcΔT

\= 10 × 0.030 × 30

Hence, Q = 9 J

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