A continuous flow water heater (geyser) has an electrical power rating of 2kW and efficiency of conversion of electrical power into heat is 80% If water is flowing through device at the constant rate of 100cc/s and the inlet temperature is 10⁰C,the outlet temperature will be (assume density remains constant)

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${13.8}^{\circ} C$

${12.2}^{\circ} C$

$30^{\circ} C$

$20^{\circ} C$

answer is B.

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Detailed Solution

$\begin{array}{l} Power P = \frac{d Q}{d t} \\ \Rightarrow P = m s \frac{d θ}{d t} (∵ d Q = m s d θ) \\ \Rightarrow \frac{80}{100} \times P = \frac{d V}{d t} \times ρ \times s \times d θ \\ \Rightarrow \frac{80}{100} \times 2000 = 100 \times 10^{- 6} \times 10^{3} \times 4200 \times (θ - 10) \\ \Rightarrow θ - 10 = 3.8 \\ ∴ θ = {13.8}^{\circ} C \end{array}$

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