An insulated tank contains 50 kg of water, which is stirred by a paddle wheel at 300 rpm while transmitting a torque of 0.1 kN-m. At the same time, an electric resistance heater inside the tank operates at 110 V, drawing a current of 2 A. Determine the rate of heat transfer after the system achieves steady state.

the rate of heat transfer after the system achieves steady state is -3.36 kW

Explanation:

Given the data in the question;

mass of water m = 50 kg

N = 300 rpm

Torque T = 0.1 kNm

V = 110 V

I = 2 A

Electric work supplied W₁ = PV = 2 × 110 = 220 W = 0.22 kW

Now, work supplied by paddle wheel W₂ is;

W₂ = 2πNT/60

W₂ = (2π × 0.1 × 300) / 60

W₂ = 188.495559 / 60

W₂ = 3.14 kW

So the total work will be;

W = 0.22 + 3.14

W = 3.36 kW

Hence total work done on the system is 3.36 kW.

At steady state, the properties of the system does not change so the heat transfer will be 3.36 KW.

The heat will be rejected by the system so the sign of heat will be negative.

i.e Q = -3.36 kW

Therefore,  the rate of heat transfer after the system achieves steady state is -3.36 kW

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