# Thermal Energy Formula

Is part of the internal energy of a thermodynamic system in equilibrium that is proportional to its absolute temperature and is increased or decreased by energy transfer, usually in the form of heat or work, through thermodynamic processes. At the microscopic level and within the framework of Kinetic Theory, it is the total of the mean kinetic energy present as the result of the random movements of atoms and molecules or thermal agitation, which disappear in the act.

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

The equation is written

Q = m*c_{p}(T_{f}-T_{i})

We have:

Q = heat transferred

m = mass

c_{p} = specific heat capacity

T_{f} = final temperature

T_{i} = initial temperature

Thermal energy Questions:

1) What energy is needed to raise the temperature of 200 grams of copper by 20 ºC if the specific heat of the copper is 386 J/kgºC?

Answer: For to know the value of the necessary energy we use the previous equation. In this case we do not have an initial or final temperature value for copper, so the temperature difference is T_{f}-T_{i} = 20 ºC, m = 200 g = 0.2 kg, c_{p} = 386 J/kgºC.

Q = m*c_{p}(T_{f}-T_{i})

Q = 0.2 kg* 368 J/kgºC* 20 ºC

Q = 1472 J.

2) How much does the temperature of 200 g of water rise, if you communicate an energy of 2500 Joules? The specific heat of the water is 4180 J/kgºC.

Answer: We cleared the temperature difference from the previous equation. Where m = 200g = 0.2 kg, Q = 2500 J, c_{p}= 4180 J/kgºC.

Q = m*c_{p}(T_{f}-T_{i})

(T_{f}-T_{i}) = Q/m*c_{p}

(T_{f}-T_{i}) = 2500 J/ (0.2 kg* 4180 J/kgºC.)

(T_{f}-T_{i}) = 2.99 ºC.

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