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Two substance \(A\) and \(B\) of same mass are heated at constant rate. The variation of temperature \(\theta\) of the substance with time \(\mathrm{t}\) is shown in the figure. Choose the correct statement
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The correct answer is:
Specific heat of \(A\) is greater than that of \(B\)
Hint : 
\(\begin{aligned} & \Delta \mathrm{H}=\mathrm{mC} \Delta \theta \\ & \frac{\mathrm{dH}}{\mathrm{dt}}=\mathrm{mC} \frac{\mathrm{d} \theta}{\mathrm{dt}} \quad \frac{\mathrm{dH}}{\mathrm{dt}}=\mathrm{a} \text { constant } \\ & \therefore \frac{d \theta}{d t} \propto \frac{1}{C} \\ & \text { i.e. slope } \propto \frac{1}{C} \quad \therefore C_B < C_A \\ & \end{aligned}\)
\(\begin{aligned} & \Delta \mathrm{H}=\mathrm{mC} \Delta \theta \\ & \frac{\mathrm{dH}}{\mathrm{dt}}=\mathrm{mC} \frac{\mathrm{d} \theta}{\mathrm{dt}} \quad \frac{\mathrm{dH}}{\mathrm{dt}}=\mathrm{a} \text { constant } \\ & \therefore \frac{d \theta}{d t} \propto \frac{1}{C} \\ & \text { i.e. slope } \propto \frac{1}{C} \quad \therefore C_B < C_A \\ & \end{aligned}\)
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