The heating element of a coffeemaker operates at 120 V and carries a current of 7.70 A. Assuming the water absorbs all of the energy converted by the resistor, calculate how long it takes to heat 0.252 kg of water from Step 1 The energy required to raise the temperature of an amount of water of mass m from T, = 23.0°C to the boiling point, T = 100°C, is Q= mC,(AT), where the specific heat of water c= 4186 J/kg - °C. We have Q = mc(AT) = m c(T - T) 0.252 kg (4186 /kg · °c)(77, 77 °c) 0.252 - 0.81225 0.812 x 10 ) Step 2 The rate P at which the heating element converts electrical potential energy into the internal energy of the water is P = (AV)I = ( J/s.

Physics for Scientists and Engineers, Technology Update (No access codes included)
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Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter27: Current And Resistance
Section: Chapter Questions
Problem 27.55P: Review. The healing element of an electric coffee maker operates at 120 V and carries a current of...
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The heating element of a coffeemaker operates at 120 V and carries a current of 7.70 A. Assuming the water absorbs all of the energy converted by the resistor, calculate how long it takes to heat 0.252 kg of water from room temperature (23.0°C) to the boiling point.
Step 1
The energy required to raise the temperature of an amount of water of mass m, from T; = 23.0°C to the boiling point, T = 100°C, is
Q = mC„(AT),
where the specific heat of water c = 4186 J/kg · °C. We have
Q = m„Cw(AT) = m„Cw(T – T;)
0.252
0.252 kg )( 4186 J/kg · °C
77
77 °c)
0.81225
0.812 x 10° J.
Step 2
The rate P at which the heating element converts electrical potential energy into the internal energy of the water is
P = (AV)I =
A
J/s.
=
Transcribed Image Text:The heating element of a coffeemaker operates at 120 V and carries a current of 7.70 A. Assuming the water absorbs all of the energy converted by the resistor, calculate how long it takes to heat 0.252 kg of water from room temperature (23.0°C) to the boiling point. Step 1 The energy required to raise the temperature of an amount of water of mass m, from T; = 23.0°C to the boiling point, T = 100°C, is Q = mC„(AT), where the specific heat of water c = 4186 J/kg · °C. We have Q = m„Cw(AT) = m„Cw(T – T;) 0.252 0.252 kg )( 4186 J/kg · °C 77 77 °c) 0.81225 0.812 x 10° J. Step 2 The rate P at which the heating element converts electrical potential energy into the internal energy of the water is P = (AV)I = A J/s. =
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