A 75 W motor rotates the propeller blades inside the calorimeter, which contains 5 L water, for 5 min. Due to the friction of the propeller blades against the water, the water is heated. Considering that all the energy went into heating the water, determine how its temperature has changed?
N = 75 W.
T = 5 min = 300 s.
V = 5 l = 5 * 10-3 m3.
ρ = 1000 kg / m3.
C = 4200 J / kg * ° C.
Let us express the amount of heat Q, which is necessary for heating water, according to the formula: Q = C * m * Δt, where C is the specific heat capacity of water, m is the mass of water, Δt is the change in water temperature.
We express the mass of heated water m by the formula: m = ρ * V, where ρ is the density of water, V is the volume of heated water.
Q = C * ρ * V * Δt.
The amount of heat Q, which is released due to the friction of the propeller blades against the water, can be expressed by the formula: Q = N * T, where = N is the engine power, T is the engine operating time.
C * ρ * V * Δt = N * T.
The change in water temperature will be determined by the formula: Δt = N * T / C * ρ * V.
Δt = 75 W * 300 s / 4200 J / kg * ° C * 1000 kg / m3 * 5 * 10-3 m3 = 1 ° C.
Answer: the water temperature in the calorimeter will increase by Δt = 1 ° C.
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