Water at temperature 400C 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=10007l/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). For water, specific heat c=4.2 kJ kg−1, K−1 latent heat of vaporization LVAP=2.268 MJ kg−1, density ρ=1000kg m−3.

Question

Water at temperature 400C  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=10007l/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). For water, specific heat c=4.2 kJ kg−1, K−1  latent heat of vaporization LVAP=2.268 MJ kg−1, density  ρ=1000kg  m−3.

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