Blocks of identical material, having masses m, 2m, 3m, 4m, and 5m are heated to 150°C, and then cooled to 50°C.
(a) Draw the nature of the graph connecting the amount of heat released vs the mass of the blocks.
(b) Write the mathematical expression that enables the determination of the specific heat capacity using the graph.
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(a) The heat energy released by a block is Q = mcΔt, where c is the specific heat capacity of the material and Δt = 150 − 50 = 100°C is the same for all the blocks.
Since c and Δt are constant, Q ∝ m. So the graph of heat released against mass is a straight line passing through the origin, as shown below.
(b) The slope of the above straight line is
$\text {slope} = \frac{\text Q}{\text m} = \text c\Delta \text t$
So the specific heat capacity is
$\text c = \frac{\text {slope of the graph}}{\Delta \text t} = \frac{\text {slope of the graph}}{100}$