Question

The resistance of an electric geyser is $14$ ohm. Current flowing is $4A.$ How much water can it heat to raise its temperature by ${10}^{o}C$ in $10$ min?

Use specific heat capacity of water $=4.186\times {10}^{3}Jk{g}^{-1}{C}^{o-1}$

• A. $.5kg$
• B. $1.6kg$
• C. $3.2kg$
• D. $2.4kg$

Answer 1

Answer: (C)

$3.2kg$

By Joule's Law, Heat produced $Q_1=I^{2}Rt$ ...............(1)

Heat transferred to water $Q_2=Ms\Delta T$ .......................(2)

Where,

I: Current, R: Resistance, t: Time,

M: Mass of water, s: specific heat capacity of water,

$\Delta T:$ Change in temperature

Assuming no loss, $Q_1=Q_2$

$I^{2}Rt=Ms\Delta T$

$M=\frac{I^{2}Rt}{s\Delta T}$

$M=\frac{4^2\times 14\times 10\times 60}{4.186\times {10}^3\times 10}$

$M=3.2kg$