120 g of water is poured into an aluminum calorimeter weighing 50 g and a 2-ohm spiral connected to a 15-volt
120 g of water is poured into an aluminum calorimeter weighing 50 g and a 2-ohm spiral connected to a 15-volt voltage source is lowered, how long will the calorimeter with water heat up by 9 degrees if energy losses to the environment can be neglected.
ma = 50 g = 0.05 kg.
Ca = 920 J / kg * ° C.
mw = 120 g = 0.12 kg.
Cw = 4200 J / kg * ° C.
R = 2 ohms.
U = 15 V.
ΔT = 9 ° C.
t -?
Heat energy Q is released in the conductor, the value of which is determined by the formula: Q = U ^ 2 * t / R.
This heat Q goes to heating the water and the calorimeter: Q = Ca * ma * ΔT + Cw * mw * ΔT = (Ca * ma + Cw * mw) * ΔT.
U ^ 2 * t / R = (Ca * ma + Cv * mv) * ΔT.
t = (Ca * ma + Cw * mv) * ΔT * R / U ^ 2.
t = (920 J / kg * ° C * 0.05 kg + 4200 J / kg * ° C * 0.12 kg) * 9 ° C * 2 Ohm / (15 V) ^ 2 = 44 s.
Answer: it takes time t = 44 s to heat water.