What is the specific heat of a substance if, when we place 6 kg of a substance at 12 Celsius in an insulated system with 9 kg of water at 99 Celsius, the system comes to a final temperature of 83.34 Celsius?
At 4180 Joules for every Kg for every Celsius degree, the water will lose
as its temperature makes the 15.66 C change from 99 C to 83.34 C. The substance therefore gains this amount.
This is
as its temperature rises from 12 C to 83.34 C, a change of 71.34 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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