1. Tardigrade
  2. Question
  3. Physics
  4. Water of volume 2 litre in a container is heated with a coil of 1 kW at 27° C. The lid of the container is open and energy dissipates at rate of 160 J / s. In how much time temperature will rise from 27° C to 77° C ? [Given specific heat of water is 4.2 kJ / kg ]

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Q. Water of volume 2 litre in a container is heated with a coil of $1\, kW$ at $27^{\circ} C$. The lid of the container is open and energy dissipates at rate of $160\, J / s$. In how much time temperature will rise from $27^{\circ} C$ to $77^{\circ} C$ ? [Given specific heat of water is $4.2\, kJ / kg$ ]

Thermal Properties of Matter

Solution:

Heat gained by the water $=($ Heat supplied by the coil)
- (Heat dissipated to environment)
$\Rightarrow m c \Delta \theta=P_{\text {Coil }} t-P_{\text {Loss}} t$
$\Rightarrow 2 \times 4.2 \times 10^{3} \times(77-27)=1000 t-160\, t$
$\Rightarrow t=\frac{4.2 \times 10^{5}}{840}=500\, sec =8\, \min 20\, \sec$