Q179 / 180 · KCET 2024 · Physics
A solid cube of mass $m$ at a temperature $\theta_0$ is heated at a constant rate. It becomes liquid at temperature $\theta_1$ and vapour at temperature $\theta_2$. Let $s_1$ and $s_2$ be specific heats in its solid and liquid states respectively. If $L_f$ and $L_v$ are latent heats of fusion and vaporisation respectively, then the minimum heat energy supplied to the cube until it vaporises is
- A$m s_1\left(\theta_1-\theta_0\right)+m s_2\left(\theta_2-\theta_1\right)$
- B$m L_f+m s_2\left(\theta_2-\theta_1\right)+m L_v$
- Correct answerC$m s_1\left(\theta_1-\theta_0\right)+m L_f+m s_2\left(\theta_2-\theta_1\right)+m L_y$
- D$m s_1\left(\theta_1-\theta_0\right)+m L_f+m s_2\left(\theta_2-\theta_0\right)+m L_v$
Solution
Minimum heat energy supplied to the cube until it vaporises, is given as
$Q=$ heat given to liquify at $\theta_1+m \times$ latent heat of fusion + heat given to vaporise at $\theta_2+m \times$ latent Heat of vaporisation
$=m s_1\left(\theta_1-\theta_0\right)+m L_f+m s_2\left(\theta_2-\theta_1\right)+m L_2$
Hence, the correct answer is option: 'C'.