Current and resistance of wire heating up water

In summary, the office worker needed to calculate the power required to warm the water to 100 degrees Celsius in 4 minutes. They did so by calculating the average power required to warm the water to 100 degrees Celsius in 4 minutes and multiplying it by the mass of the water (250 grams). They then determined the required resistance in the heating element at 100 degrees Celsius by dividing the average power by the mass of the water.
  • #1
Shelby8
5
0

Homework Statement


An office worker uses an immersion heater to warm 250 g of water in a light, covered, insulated cup from 20 degrees C to 100 degrees C in 4 minutes. The heater is Nichrome resistance wire connected to 120V power supply. Assume wire is at 100 degree C during 4 minute time interval.

a) calculate average power required to warm the water to 100 degree C in 4 min
b) calculate the required resistance in the heating element at 100 degree C
c) calculate the resistance of the heating element at 20 degree C
d) derive a relationship between the diameter of the wire, resistivity at 20 degree C, rou (po), the resistance at 20 degree C, Ro, and the length L
e) If L = 3 m, what is the diameter of the wire?

What we are given:
mass of water = 250 g
density of water = 1000 kg / m^3
change in T = 80
V = 120V
t = 4 minutes
p of Nichrome = 150 *10^-8
coeff of resistivity of Nichrome = 0.4 * 10^-3

Homework Equations


P = I*V = V^2/I = I^2*R
R = V/I
R = Ro [1 + coefficient of resistivity (T - To)]
R = p L / A
I = Q / t

The Attempt at a Solution


a) calculate average power required to warm the water to 100 degree C in 4 min
density = m / v ... v = m / density
v = A * L
v = 250 / 1000 = .25 m ^3 = A * L
R = p L / (.25/L) = p L^2 / .25

How do I calculate I for Power without knowing the charge?
 
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  • #2
Shelby8 said:
How do I calculate I for Power without knowing the charge?
You should know (or be able to look up) an expression that relates power to voltage and current. Of course, you'll need to have completed part (a) to find the power requirement first.
 
  • #3
If the wire is at 100C then it can't heat the water in 4 minutes or any other finite amount of time ...
 
  • #4
+1

I suspect a badly designed question. I think they said to assume the wire is at a constant temperature so you would ignore it's thermal mass.
 
  • #5
CWatters said:
+1

I suspect a badly designed question. I think they said to assume the wire is at a constant temperature so you would ignore it's thermal mass.
Either that or the office worker wanted a long rest pause ... :smile:
 

FAQ: Current and resistance of wire heating up water

What is the relationship between current and resistance in heating up water?

The relationship between current and resistance in heating up water is described by Ohm's Law, which states that the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance. This means that as the current increases, the resistance of the wire decreases, resulting in more heat being produced in the water.

How does the type of wire affect the resistance and heating of water?

The type of wire used can greatly affect the resistance and heating of water. Different materials have different resistivity values, which determines how much resistance the wire will have. Materials with higher resistivity will produce more heat compared to materials with lower resistivity.

What is the role of wire thickness in heating up water?

The thickness of the wire also plays a role in heating up water. Thicker wires have lower resistance compared to thinner wires, which means they can carry more current and produce more heat. However, there is a limit to how much current can flow through a wire, so using excessively thick wires may not necessarily result in more heat produced.

Does the length of the wire impact the heating of water?

Yes, the length of the wire does impact the heating of water. Longer wires have higher resistance compared to shorter wires, which means they will produce less heat. This is why it is important to use the appropriate length of wire to achieve the desired amount of heat in the water.

What other factors should be considered when using wire to heat up water?

Aside from the type, thickness, and length of the wire, other factors that should be considered include the voltage and current of the power source, the material and volume of the water, and the environmental conditions. These factors can all affect the resistance and heating capabilities of the wire, and should be taken into account when designing experiments or systems involving heating water with a wire.

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