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Shelby8

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## 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?