Question #3629f

1 Answer
José Roberto Pereira
Oct 19, 2015

See example below:

Explanation:

Supose you want to heat 2 liters of water using an electric heater.
The water has to be heated from #20^(o)C# to #80^(o)C# and the heater has a resistance of 30 ohms to be connected to a power supply of 120Volts.
The heater is thermal insulated from the environment.
How much time wil be taken to do the job?

First, we have to calculate the work, in calories:

#tau# = m.c. #Delta theta#

where:

#tau# = work in calories
m = mass in (g)
c = specific heat of water = 1
#Delta theta# = temperature difference (#theta_2-theta_1)#
#Delta theta# = #80-20=60^(o)C#

As the water specific mass=1, 2 liters of water have 2000g
(m=2000g).

#tau=2000xx1xx60# = 120000 calories

The electrical power of the heater is:

#P=V^2/R = 120^2/30=480# Watts

The electrical work in Joules is equal to:

#W=P.t#

where:

W = Electrical Work, in Joules
P = Electrical Power, in Watts
t = time, in seconds

To convert calories in Joules, we use the equation:

#tau=0.239xxPxxt#

#120000=0.239xx480xxt#

#t=120000/(0.239xx480)#

#t ~= 1046 s ~= 17 min 26 s#

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