Two substances A and B of same mass are heated at constant rate. The variation of temperature θ of the substances with time t is shown in the figure. Choose the correct statement.
Specific heat of A is greater than that of B.
When heat is supplied at a constant rate to a body without change of state, the temperature rises linearly with time, and the rate of rise is inversely proportional to the heat capacity of the body. For equal masses, the steeper graph belongs to the substance with the smaller specific heat.
Step 1 — Heat supplied in time t at rate P: \(Pt = mc\,\theta\), so \(\theta = \dfrac{P}{mc}\,t\).
Step 2 — Slope of the θ–t line: \(\dfrac{d\theta}{dt} = \dfrac{P}{mc} \propto \dfrac{1}{c}\) for the same P and m.
Step 3 — The line for B is steeper than the line for A, so \(\dfrac{1}{c_B} \gt \dfrac{1}{c_A}\), i.e. \(c_A \gt c_B\).
B having the larger specific heat would require B's line to be the gentler one, which is the reverse of the figure. Equal specific heats would make the two lines coincide, and since a definite comparison follows from the graph, the statement that none is true also fails.
Specific heat of A is greater than that of B. option is correct.
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