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Thermal Energy Formula

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  • Difficulty Level : Easy
  • Last Updated : 09 Mar, 2022
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Thermal energy is the energy that exists within a system. It’s in charge of maintaining the system’s temperature. Heat is the transfer of thermal energy. Thermodynamics is a discipline of physics that studies the transport of heat between different types of systems. It also concerns the manner in which the task is completed throughout the procedure. 

Thermal Energy

The energy obtained from heat is referred to as thermal energy. The movement of small particles within the system usually causes the heat produced by thermal energy. It’s the energy that allows heat to circulate within a system. In most cases, heat is generated as particles move around within an object.

Thermal energy is responsible for the system’s temperature and is a component of the system’s total energy, which is made up of potential and kinetic energy. Q is a common way of expressing thermal energy. Its mass, temperature difference, and specific heat are all directly proportional.

Thermal energy is measured in Joules, a SI unit of measurement (J).

Formula of Thermal Energy

The formula for thermal energy is as follows:

Q = mcΔT

Where,

  • Q = Thermal Energy
  • m = Give substance Mass
  • c = Specific heat
  • ΔT = Difference in Temperature

Derivation of the Formula

We have,

Specific heat capacity = (Thermal energy input) / ((mass) × (Temperature change))

However, because the formula requires special symbols, we can say that C stands for specific heat capacity, T stands for temperature, and Et stands for thermal energy. It’s vital to realize, however, that T isn’t used as a stand-alone phrase; rather, it represents the change in T through time. ΔT is the most common symbol for change is Δ. Meanwhile, we can suppose that the input is the amount that determines the change in thermal energy, which is denoted by ΔEt.

Thus, c = (ΔEt)/(m × ΔT)

ΔEt = mcΔT

Sample Problems

Question 1. A substance’s mass is specified as 16 kg, and its specific heat is 0.068 J/kg °C. The temperature difference is indicated as 23°C. Determine the substance’s thermal energy based on the data.

Answer: 

Given: m = 16 kg, c = 0.068 J/kg °C, ΔT = 23°C.

Since,

Q = mcΔT

∴ Q = 16 × 0.068 × 23

Q = 25.02 Joules

Question 2. Assume that a 12 kg substance changes temperature by 55 degrees Celsius, with a specific heat of 0.04 J/kg °C. Determine the thermal energy of the compounds using the given information.

Answer:

Given: m = 12 kg, c = 0.04 J/kg °C, ΔT = 55°C.

Since,

Q = mcΔT

∴ Q = 12 × 0.04 × 55

Q = 26.4 Joules

Question 3. When you communicate the energy of 1800 Joules, how much does the temperature of 263 g of water rise? Water has a specific heat of 3482 J/kg°C.

Answer:

Given: m = 263 g = 0.263 kg, c = 3482 J/kg °C, Q = 1800 Joules

Since,

Q = mcΔT

∴ ΔT = Q/mc

∴ ΔT = (1800) / (0.263 × 3482)

∴ ΔT = 1800 / 915.8

ΔT = 1.965 °C.

Question 4. If the specific heat of copper is 453 J/kg°C, how much energy is required to raise the temperature of 0.36 kg of copper by 23°C?

Answer:

Given: m = 0.36 kg, c = 453 J/kg °C, ΔT = 23°C.

Since,

Q = mcΔT

∴ Q = 0.36 × 453 × 23

Q = 3750.8 Joules

Question 5. The mass of a substance is 20 kg, and its thermal energy is 686 J. The difference in temperature is given as 23°C. Based on the facts, determine the specific heat.

Answer:

Given: m = 20 kg, Q = 686 J, ΔT = 23°C

Since,

Q = mcΔT

∴ c = Q/mΔT

∴ c = (686) / (20 × 23)

∴ c = 686 / 460

c = 1.491 J/kg °C

Question 6. Determine the amount to which the temperature of 23 kg of water will rise after transmitting around 1900 Joules of energy, using the specific heat of water of 3820 J/kg °C.

Answer:

Given : m = 23 kg, c = 3820 J/kg °C, Q = 1900 Joules

Since,

Q = mcΔT

∴ ΔT = Q/mc

∴ ΔT = (1900) / (23 × 3820)

∴ ΔT = 1900 / 8786

ΔT = 0.2162 °C.

Question 7. What is the SI unit of Thermal Energy?

Answer:

SI unit of Thermal Energy is Joules.

Question 8. Explain the Formula of Thermal energy.

Answer:

The formula for thermal energy is as follows :

Q = mcΔT

Where,

  • Q = Thermal Energy
  • m = Give substance Mass
  • c = Specific heat
  • ΔT = Difference in Temperature
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