A 2.80 102 W electric immersion heater, P, is used to heat a cup of water, as sh

Question

A 2.80 102 W electric immersion heater, P, is used to heat a cup of water, as shown in Figure 12-20. The cup is made of glass and its mass is 3.00 102 g. It contains 225 g of water, m, at 15°C. How much time is needed to bring the water to the boiling point? Assume that the temperature of the cup is the same as the temperature of the water at all times and that no heat is lost to the air.

Explanation / Answer

1)By KE = Q = 1/2Mv^2 =>m x s x delta T = 1/2 x M x v^2 =>15 x 450 x delta T = 1/2 x 720 x 25 x 25 =>delta T = 33.33*C 2)Q(total) = Qwater(15*C to 100*C) + QGlass(15*C to 100*C) =>Q(t) = m(water) x s(water) x 85 + m(Glass) x s(water) x 85 =>Q(t) = 85[225 x 4.18 + 300 x 0.84] = 101362.5 J Let the required energy is provided by the heater in t second =>P x t = 101362.5 =>t = 101362.5/270 = 375.42 sec

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