Question

A hot liquid contained in a container of negligible heat capacity loses temperature at rate $3K/min$ just before it begins to solidify. The temperature remains constant for $30$ min. If the ratio of specific heat capacity of liquid to specific latent heat of fusion is $\frac{x}{90}{K}^{-1}$. Find $x$. (given that rate of losing heat is constant).

Answer 1

Rate of cooling during solid phase:$\frac{dQ}{dt}=msd\theta$ where s is the specific heat, m is the mass of thr sustance and $d\theta$ is the temp difference.
Rate of cooling during phase change: $\frac{mL}{30}$ where L is the latent heat of fusion
Given the rate of cooling is same for both.
$\therefore msd\theta =\frac{mL}{30}$
$\therefore \frac{s}{L}=\frac{1}{3\times 30}=\frac{1}{90}{K}^{-1}$