Temperature change time base problem. Suppose V = 28 V, I = 0.1 A, mw = 54 gm, cw = 4.18 J/gm K, mr = 10 gm, and cr = 3.7 J/gm K. If the water is initially at room temperature, how long will it take for the water to heat up 2 K? (Hint: dT/dt is approximately equal to T / t .)
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Power output of heater = VI = 28 x 0.1 = 2.8W
Energy needed to heat water = 54 x 4.18 x 2 = 451.44J
Energy needed to heat 'r' (whatever that is - you don't say) = 10 x 3.7 x 2 = 74J
Total energy needed = 451.44 +74 = 525.44J
P = E/t so t = E/P = 525.44/2.8 = 188s
Energy needed to heat water = 54 x 4.18 x 2 = 451.44J
Energy needed to heat 'r' (whatever that is - you don't say) = 10 x 3.7 x 2 = 74J
Total energy needed = 451.44 +74 = 525.44J
P = E/t so t = E/P = 525.44/2.8 = 188s