Answer: Cs = [m1c1(T - T1) + mcCc(T - Ts)]/Ms(Ts - T)
Step-by-step explanation:
The concept of heat exchange which is expressed as
heat lost by a hot body = heat gained by a cold body
The specific heat of a solid substance as determined by the method of mixture using the heat exchange concept would be
Heat lost by substance = heat gained by liquid + heat gained by calorimeter
Thus,
MsCs(Ts - T) = m1c1(T - T1) + mcCc(T - Tc)
Dividing both sides by Ms(Ts - T)
The formula for calculating the specific heat capacity by method of mixtures is
Cs = [m1c1(T - T1) + mcCc(T - Ts)]/Ms(Ts - T)
Where
m1 = mass of liquid
c1 = specific heat of liquid
ms = mass of substance
Cs =specific heat of substance
mc = mass of calorimeter
Cc = specific heat of material used in making the calorimeter
T = Final temperature of the mixture
T1 = initial temperature of the liquid
Ts = initial temperature of the substance