Water Level remains constant!

Classical Mechanics Level 5

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

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 minimum power \(P\) (in \(MW\)) that must be generated as heat in the steady state in resistor \(R\) 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 \(c = 4.2 kJ kg^{–1} K^{–1}\), latent heat of vaporization \(L_{vap} = 2.268 MJ kg^{–1}\), density \(\rho = 1000 kg m^{–3}\).


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