Question

In an experiment on the specific heat of a metal a 0.20 kg block of the metal at ${150}^{o}C$ is dropped in a copper calorimeter (of water equivalent 0.025 kg) containing $150c{m}^3$ of water at ${27}^{o}C$. The final temperature is ${40}^{o}C$. Compute the specific heat of the metal. If heat losses to the surroundings are not negligible, is your answer greater or smaller than the actual value for specific heat of the metal ?

Answer 1

Mass of the metal, m = 0.20 kg = 200 g
Initial temperature of the metal, $T_1$ = 150 ${}^o$C
Final temperature of the metal, $T_2$ = 40 ${}^o$C
Calorimeter has water equivalent of mass, m = 0.025 kg = 25 g
Volume of water, V = 150 cm${}^3$
Mass (M) of water at temperature T = 27${}^o$C:
$150\times 1=150g$

Fall in the temperature of the metal:

$\Delta T_m=T_1$-$T_2$ $=150-40=110{}^{o}C$
Specific heat of water, $C_w=4.186J/g/K$
Specific heat of the metal $=C$
Heat lost by the metal, $=mCT$ .... (i)
Rise in the temperature of the water and calorimeter system: $T_1-T=40-27=13{}^{o}C$
Heat gained by the water and calorimeter system: $=m_1{C}_{w}T=(M+m)C_{w}T$ ....(ii)

Heat lost by the metal = Heat gained by the water and colorimeter system

$mC\Delta T_m=(M+m)C_w{T}_w$

$200\times C\times 110=(150+25)\times 4.186\times 13$

$C=(175\times 4.186\times 13)/(110\times 200)=0.43J{g}^{-1}{k}^{-1}$

If some heat is lost to the surroundings, then the value of C will be smaller than the actual value.