A flow calorimeter is used to measure the specific heat of a liquid. Heat is added to a known rate to a stream of the liquid as it passes through the calorimeter at a known rate. Then a measurement of the resulting temperature difference between the inflow and the outflow points of the liquid stream enables us to compute the specific heat of the liquid. A liquid of density $0.2 g / c m^{3}$ flows through a calorimeter at the rate of $10 c m^{3} / s$ . Heat is added by means of a $250$ Watt electric heating coil, and a temperature difference of $25^{\circ} C$ is established in steady-state conditions between the inflow and the outflow points. Find the specific heat of the liquid.

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Solution

Density of liquid = 0.2gm/ $c m^{3}$
$θ = m c Δ T$ ( $θ$ =heat flow)
$θ = D \times V \times C \times Δ T$ (D=density,V=volume,C=Thermal capacity)
Differentiating
$\frac{d θ}{d t} = 0.2 \times 10 \times C \times 25$
$250 = 50 \times C$
$C = 5 c a l / g m ° C$

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