Question

Equal heat is given to two objects $A$ and $B$ of mass $1g$ temperature of $A$ increase by $3^{o}C$ and $B$ by $5^{o}C.$ which object has more specific heat? and by what factor?

Answer 1

$S=\frac{\Delta Q}{m\Delta T}$
Let $Q$ cal of heat is given to both $A$ and $B$.

For body $A$,
$S_1=\frac{Q}{1\times 3}=\frac{Q}{3}cal$ $g^{-1}$ ${}^0{C}^{-1}$

For body $B$,
$S_2=\frac{Q}{1\times 5}=\frac{Q}{5}cal$ $g^{-1}$ ${}^0{C}^{-1}$

Now,
$\frac{S_1}{S_2}=\frac{Q/3}{Q/5}=\frac{5}{3}$
$\Rightarrow S_1=\frac{5}{3}{S}_2$

Thus, specific heat capacity of body $A$ is more than body $B$ and by a factor of $\frac{5}{3}$.