Current and resistance of wire heating up water

[Shelby8]

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?

 

[gneill]

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.

 

[rude man]

If the wire is at 100C then it can't heat the water in 4 minutes or any other finite amount of time ...

 

[CWatters]

+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.

 

[rude man]

+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 ...