KCET · Physics · Thermal Properties of Matter
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 \(m L_f+m s_2\left(\theta_2-\theta_1\right)+m L_v\)
- C \(m s_1\left(\theta_1-\theta_0\right)+m L_f+m s_2\left(\theta_2-\theta_1\right)+m L_y\)
- D \(m s_1\left(\theta_1-\theta_0\right)+m L_f+m s_2\left(\theta_2-\theta_0\right)+m L_v\)
Answer & Solution
Correct Answer
(C) \(m s_1\left(\theta_1-\theta_0\right)+m L_f+m s_2\left(\theta_2-\theta_1\right)+m L_y\)
Step-by-step Solution
Detailed explanation
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
\(=m s_1\left(\theta_1-\theta_0\right)+m L_f+m s_2\left(\theta_2-\theta_1\right)+m L_2\)
\(Q=\) 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
\(=m s_1\left(\theta_1-\theta_0\right)+m L_f+m s_2\left(\theta_2-\theta_1\right)+m L_2\)
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