Water of volume \(2\, L\) in a closed container is heated with a coil of \(1\,kW\). While water is heated, the container loses energy at a rate of \(160\, J/s\) . In how much time will the temperature of water rise from \(27\,^oC\) to \(77\,^oC\) ? (Specific heat of water is \(4.2\, kJ/kg\) and that of the container is negligible)

In \(1\,sec\) heat gained by water

\( = 1\,K\,W - 160J/s\)

\( = 1000\,J/s - 160\,J/s\)

\( = 840\,J/s\)

Total heat required to raise the temperature of water \(\left( {volume\,2L} \right)\,from\,{27^ \circ }c\,to\,{77^ \circ }c\)

\( = {m_{water}} \times sp.ht{\rm{\backslash }}\Delta \theta \)

\( = 2 \times {10^3} \times 4.2 \times 50\)

                                   \(\left[ {mass = density \times volume} \right]\)

\(And,840 \times t = 2 \times {10^3} \times 4.2 \times 50\)

\(or,\,\,\,\,\,\,\,\,\,t = \frac{{2 \times {{10}^3} \times 4.2 \times 50}}{{840}}\)

\(500s = 8\,\min \,20s\)