Some stoves use the heat produced by current flowing through a conductor. If the heating element (conductor) has a resistance of 30 ohms, how long will the burner have to work to heat 500 g of 30°C water up to its boiling point? The specific heat of water is 4.19 x 103 J/kg·°C, and the household voltage is (120V).
I think I use this formula at some point:
H=I^2Rt
but that's really all I know about solving this, can someone please help??
yes, true
power = V i but V = i R
so
Power = i^2 R = V^2/R Joules per second or "Watts"
Energy (or heat) = Power * time
so indeed
H = i^2 R t = V^2/R Joules
Now how much heat do we need?
H = mass * specific heat * change in temp
H = 0.5 * 4.19*10^3 * 70 Joules
so in the end
(120^2/30) * t = 35 * 4.19*10^3
t is in seconds
To solve this problem, you can use the formula for heat transfer:
Q = mcΔT
where:
Q is the heat transferred (in joules)
m is the mass of the substance (in kilograms)
c is the specific heat capacity of the substance (in joules per kilogram per degree Celsius)
ΔT is the change in temperature (in degrees Celsius)
In this case, you are given:
m = 500 g = 0.5 kg (since 1 kg = 1000 g)
c = 4.19 x 10^3 J/kg·°C
ΔT = Boiling point (100°C) - Initial temperature (30°C) = 70°C
Now, you need to calculate the heat transferred which can be done using the formula mentioned above.
Q = mcΔT
Q = (0.5 kg) x (4.19 x 10^3 J/kg·°C) x (70°C)
Q = 1.4585 x 10^5 J
Now, you know the heat transferred, next we can use the power equation to calculate the time required.
P = VI,
where P is the power (in watts), V is the voltage (in volts), and I is the current (in amperes).
Since the voltage is given as 120V, and the resistance is given as 30 ohms, you can find the current using Ohm's Law:
I = V/R
I = 120V / 30Ω
I = 4 amperes
Now, you have the current value. You can determine the power using the following formula:
P = VI
P = (4A) x (120V)
P = 480 watts
Finally, use the power formula to determine the time required:
P = H/t,
where H is the heat transferred (in joules) and t is the time (in seconds).
Rearrange the formula to solve for t:
t = H / P
t = (1.4585 x 10^5 J) / (480 W)
t ≈ 304 seconds or approximately 5.07 minutes.
To summarize, the burner will need to work for approximately 5.07 minutes to heat 500 g of 30°C water up to its boiling point, assuming a resistance of 30 ohms and a household voltage of 120V.