If 10 kg of a substance are placed in an insulated system with 15 kg of water, with the substance originally at 20 and the water at 93 Celsius, then if the system comes to a final temperature of 84.24 Celsius, what is the specific heat of the substance?
At 4180 Joules for every Kg for every Celsius degree, the water will lose
as its temperature makes the 8.760002 C change from 93 C to 84.24 C. The substance therefore gains this amount.
This is
as its temperature rises from 20 C to 84.24 C, a change of 64.24 C.
The change per unit mass per degree is thus substance gain per mass unit per degree:
If mass m1 of a substance with specific heat c1 at temperature T1 is placed in a closed system with a mass m2 of another substance with specific heat c2 at temperature T2, then the two substances will exchange thermal energy until they arrive at a common temperature Tf. Since the system is closed, there will be known net change in the thermal energy of the system.
The net change in the thermal energy of the system is equal to the sum of the change in the thermal energy of the first substance and the change in the thermal energy of the second substance. This net change is
net change in thermal energy = m1 c1 (Tf - T1) + m2 c2 (Tf - T2) = 0.
If all the quantities but one are known (as in this case where only Tf is unknown), this expression of energy conservation can easily be solved for that unknown quantity.
If any of the quantities m1, c1, T1, m2, c2, T2 or Tf is unknown and all the rest known, then the unknown quantity can easily be found.
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