Subsystem 1 has a mass M 1 , a specific heat c 1 and is initially at temperature

Question

Subsystem 1 has a mass M1 , a specific heat c1 and is initially at temperature T1 when it is placed in thermal contact with Subsystem 2 having a mass M2, specific heat c2 and initial temperature T2i. Assume that system comprised of the two subsystems is thermally isolated from the rest of the universe and that neither subsystem experiences a phase change as they reach thermal equilibrium with one another. The system eventually reaches an equilibrium temperature of Teq. Derive an algerbraic expression for the specific heat, c2 of Subsystem 2 in terms of the other quantities.

Explanation / Answer

let the final temp of the both systems = T.

I am assuming that mass m1 is inital less temp as co pare to mass m2

Heat gained by mass m1 = heat lost by mass m2

m1 C1 (Teq-T1) = m2 C2 ( T2i - Teq)

solving the above expression,

[m1 C1 (Teq-T1)] /[m2 (T2-Teq)] = C2

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