Answer:
100 min
Explanation:
Energy is equal to the product of power and time. The energy needed to increase the temperature of water is equal to the product of the mass of the water, the specific heat capacity of water, and the temperature increase.
The relevant equations are:
E = Pt
E = mCΔT
where E is energy,
P is power,
t is time,
m is mass,
C is specific heat capacity,
and ΔT is change in temperature.
Since C and ΔT are constant, we can show that energy per mass is constant.
E / m = CΔT
E / m = constant
E₁ / m₁ = E₂ / m₂
Substituting the expression for energy:
P₁ t₁ / m₁ = P₂ t₂ / m₂
Plugging in values:
(2.5 kW) (2 min) / (1.7 kg) = (5.0 kW) t₂ / (170 kg)
t₂ = 100 min
It takes 100 minutes for the heater to raise the temperature of the water.
