Simple Heat calculation and Black Principle

Temperature of matter can be increased or decreased by heat or cool it. If a matter is heated, it means amount of energy is received by the matter, then the temperature increase. For example, when we heat water on the stove, heat energy is transferred from stove to water, then increase water temperature. The question is:  How much energy is required to increase temperature?

Heat energy required to increase the temperature can be calculated by this equation:

Q = m.c.∆T

Where:

Q: Heat energy

m: Mass

c: specific heat

∆T: Temperature difference

Each matter has different specific heat value, such as water has specific heat 4200 J/kgC. It means we need 4200 Joules of energy to increase 1 Celsius for 1 kg of water.

For example, we want to heat 1 kg of water from 20 Celsius to 50 Celsius. Heat energy we need is:

Q = m.c.∆T

Q= 1 kg . 4200 J/kgC . (50-20) = 126000 Joules

How about calculation of mixing temperature of matter?

Assume we mix 1 kg water at 20 Celsius and 2 kg water at 80 Celsius, How is the temperature of the mixing water?

“Black” principle said heat received is equal heat given. So the equation is:

Q₁ = Q₂   (Q₁ means heat given and Q₂ means heat received)

This condition resulting heat transfer from higher temperature to lower temperature, so water at 80 Celsius gives heat to water at 20 Celsius. Let’s say T_mix is final temperature after mixing water, then

m₁.c₁.∆T₁ = m₂.c₂.∆T₂

2 . 4200. (80-T_mix)= 1 . 4200 . (T_mix-20)

8400 . (80-T_mix) = 4200 . (T_mix-20)

672000-8400 T_mix=4200 T_mix-84000

Then we can get T_mix= 60 Celsius.