Water Level remains constant!

Water at temperature 40 ° C 40°C flows from a tap T T into a heated container C C . The container has a heating element (a resistor R R ) which is generating heat at the rate of P P , that may be varied. The rate of water in flow from tap is m = 1000 7 L / m i n m = \frac{1000}{7} L/min .

The heat generated is sufficient so that the water in the container is boiling and getting converted into steam at a steady rate. What is the power P P (in M W MW ) that must be generated as heat in the steady state in resistor R R so that the amount of liquid water in the container neither increases nor decreases with time ?

(Neglect other losses of heat, such as conduction from the container to the air and heat capacity of container)

Note - For water, specific heat c = 4.2 k J k g 1 K 1 c = 4.2 kJ kg^{-1} K^{-1} , latent heat of vaporization L v a p = 2.268 M J k g 1 L_{vap} = 2.268 MJ kg^{-1} , density ρ = 1000 k g m 3 \rho = 1000 kg m^{-3} .


The answer is 6.

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3 solutions

Nishant Rai
Jun 10, 2015

Shubham Maurya
Nov 28, 2015

I think minimum power is required when steam is leaving at 100 degC itself, though the temperature of steam is not mentioned in question.

Satvik Choudhary
Jun 10, 2015

Shouldn't the power be asked in kW.

Nishant Rai made the answer as sample as possible. If it was asked in kW , answer would be 6000 , which is not so simple as 6.

Muhammad Arifur Rahman - 5 years, 8 months ago

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