# Thermal Energy Formula

## Thermal Energy Formula

The energy produced by heat is referred to as thermal energy. The movement of tiny particles within an object causes it to heat up. The amount of heat produced increases with the speed of the particles. The system’s temperature is controlled by thermal energy, which is also a component of the system’s overall energy, which is made up of kinetic and potential energy. Typically, Q is used to express thermal energy. The mass of the substance, the difference in temperatures, and the specific heat all directly relate to it. Joules is the thermal energy SI unit (J).

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### Nature of Thermal Energy

In almost all real-world physical systems, energy transfer occurs with an efficiency of less than 100%, producing some thermal energy. Low-level thermal energy is the typical form of this energy. Low-level here means that the temperature associated with thermal energy is very close to ambient temperature. Only when there is a temperature difference can the work be extracted. The low-level thermal energy, however, signifies “the end of the road” for the energy transfer.

### Derivation

Specific Heat Capacity = thermal energy input/(mass)×(temperature change)

We will use the symbols C for specific heat capacity, T for temperature, and Et for thermal energy to represent this equation. But rather than T directly, the equation takes into account T’s variation during the energy-input procedure. The Greek letter delta (∆) is the standard symbol we use for the “change,” so the change in T is written as ∆T. The amount by which the thermal energy changes is referred to as the thermal energy input, according to ∆Et.

Using these abbreviations, the equation now becomes:

C=∆Et/m.∆T

Often it is useful for rearranging this equation to solve for the change in thermal energy:

∆Et=m.C.∆T

For example, to increase the temperature of a 10-kg wooden chair from 20◦C to 25◦C, it would need an energy input of:

∆Et=m.C.∆T= (10kg) (1700J/kg.∘C) (5∘C) = 85,000J.

(Notably, the official units of ‘C’ are joules/kg per degree Celsius.)

Water is fundamental to us as humans even though it is not inherently special. Additionally, our culture spends a significant amount of energy heating water for a variety of uses. Therefore, it’s a good idea to keep in mind the significance of water’s specific heat capacity:

Cwater=4200 J/kg.∘C  =1 kcal/kg.∘C = 1 Btu/lb.∘F

The last two numbers come from the definitions of the kilocalorie and Btu units, respectively. It’s also helpful to know that a kilogram of water occupies a volume of one litre (just over a quart), whereas a pound of water can occupy a volume of one pint because the quantity of water is frequently measured by volume rather than by mass (two cups, or half a quart). There are eight pints (pounds) or 3.8 litres in a gallon of water (kilograms).

The Thermal Energy Formula is extremely essential for students to learn. Having a well-rounded understanding of derivations helps students understand the concepts of the chapter well. Students can find the Thermal Energy Formula from the website and mobile application of Extramarks. Extramarks’ study resources on Thermal Energy Formula explain each and every step in a detailed manner. Students can trust the Thermal Energy Formula study resources provided by Extramarks, as expert subject teachers write them. With the help of Thermal Energy Formula solved examples, students can learn any topic well. They should therefore refer to solved questions of Thermal Energy Formula to understand this topic well. Extramarks provides NCERT solutions to help students solve questions. Students can refer to the NCERT solutions for this topic to refer to solved examples.

### Solved Examples on Thermal Energy Formula

Question

Suppose the person shown in Figure 1 pushes the box, maintaining a constant velocity. The box has a mass of 100 kg and moves through a distance of 100 m. The coefficient of kinetic friction between the box and floor is μκ = 0.3. what amount of thermal energy is transferred to the box-floor system?

Solution:

Since the box is not accelerating (it has constant velocity) and the force on the box is in the same direction as the direction of motion (no vertical component), the net force due to the person is exactly balanced by the force due to friction. This force applied over the given distance gives the change in thermal energy of the system.

ΔET=0.3.9.81m/s2.100kg.100m

= 29.43 kJ

Question

Suppose the paddle wheel depicted in Figure 2 is rotated by an electric motor which is rated at 10 W output power for 30 minutes. What is the amount of thermal energy that is transferred to the water?

Solution:

In this system, all the energy eventually is transferred to the thermal energy of the water (assuming the heat capacity of the paddles is negligible).

ET = Power . Duration

=10W. (30. 60s)

= 18 kJ.