physics helpp??

Question

The heating coil of a hot-water heater has a resistance of 20 and operates at 210 V. If electrical energy costs $0.080/kWh, what does it cost to raise 270 kg of water in the tank from 15°C to 72°C?

Answer 1

We assume no heat losses to the environment.

P=V^2/R
Q=m Cp (T2-T1)

$=cost x Q (we don't need electric power unless you what to compute how long it takes)

Cp=4.186 joule/(gram x degree C)
Cp=4,186 Joules/ (kg x degree C)
$=(cost per unit ) m Cp (T2-T1)
cost per unit=[0.080/ 1000 3600] = 2.22 e-8 $/Joules
$=[2.22 e-8 ] x 270 kg x 4186 (72-15)=$0.025116

P=W/t
t=W/P
W=Q=Q=m Cp (T2-T1)
P=V^2/R
t=R m Cp (T2-T1)/V^2
t=20 x 270 x 4,186 (72-15)/(210^2)
t=29217 sec
t=487min
T=8.1h
I'm getting a gas heater!