Question

How much power is required by an electric heater to melt $5$ kg of ice at $0^{\circ }C$ in $2$ mins if $60\%$ heat is supplied by the heater? ($L=336$ J/g)

• A. 28kW
• B. 59kW
• C. 93kW
• D. 102kW

Answer 1

Answer: (C)

93kW

Given: mass of ice $\left(m\right)=5kg$, time $\left(t\right)=2min=120$ s, efficiency of heater = $60\%$, $L=336$ J/g = $336\times {10}^{3}J{kg}^{-1}$.
If $P$ watt is the power supplied by the heater, then energy supplied by the heater in $t$ sec = $P\times t$ Joule
Since the efficiency of the heater is $60$%, only $60$% of its energy is utilized to melt the ice
$60$% of $Pt=mL$
$60/100\times P\times 30=5\times 336\times {10}^3$
$0.6\times P\times 30=5\times 336\times {10}^3$
$P=5\times 336\times {10}^3/0.6\times 30$
$P=93\times {10}^{3}watt$ or 93 kW