To calculate the time it will take for a heating coil to heat a given amount of water, we can use the formula:
Q = mcΔT
where Q is the heat energy transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
In this case, we have:
m = 1.4 kg
c = 4200 Jkg^(-1)K^(-1)
ΔT = (100°C – 30°C) = 70°C
First, we need to calculate the heat energy required to raise the temperature of the water from 30°C to 100°C:
Q = mcΔT
Q = (1.4 x 4200 x 70)J
Q ≈ 411,600 J
Now, we can calculate the time it will take for the heating coil to transfer this amount of heat energy. The power (P) of the heating coil is given as 70 W (watts).
The relationship between power, energy, and time is:
P = ΔE/Δt
where P is power, ΔE is change in energy, and Δt is change in time.
In this case, we know that ΔE = Q (heat energy transferred) and P = 70 W. We can rearrange the equation to solve for Δt:
Δt = ΔE/P
Δt ≈ 411,600 J / 70 W
Δt ≈ 5880 seconds
Therefore, it will take approximately 5880 seconds or 98 minutes to heat 1.4 kg of water from 30°C to 100°C using a heating coil rated at 70 W.
