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An electric heater has a resistance of 12 ohm and is operated from a 220 V power line. If no heat escapes from it, how much time is required to raise the temperature of 40 kg of water from 15 degree Celsius to 80 degree Celsius?
Most Upvoted Answer
An electric heater has a resistance of 12 ohm and is operated from a 2...
Calculating the Amount of Heat Required
To determine the amount of heat required to raise the temperature of the water, we can use the specific heat capacity formula:
Q = m * c * ΔT
Where:
Q is the amount of heat energy
m is the mass of the water
c is the specific heat capacity of water
ΔT is the change in temperature
Calculating the Mass of Water
Given:
Mass of water (m) = 40 kg
Calculating the Specific Heat Capacity of Water
The specific heat capacity of water is approximately 4.186 J/g°C.
Calculating the Change in Temperature
The change in temperature (ΔT) is the difference between the final temperature and the initial temperature.
Given:
Initial temperature = 15°C
Final temperature = 80°C
ΔT = 80°C - 15°C = 65°C
Calculating the Amount of Heat Required
Using the values we have gathered, we can now calculate the amount of heat required to raise the temperature of the water.
Q = m * c * ΔT
Q = 40 kg * 4.186 J/g°C * 65°C
However, we need to convert the units of mass from kg to grams and the specific heat capacity from J/g°C to J/°C.
1 kg = 1000 g
1 J/g°C = 1 J/g°C * 1000 g/kg = 1000 J/°C
Q = 40,000 g * 4.186 J/°C * 65°C
Q = 10,396,400 J
Calculating the Power of the Electric Heater
The power (P) of an electric heater can be calculated using the formula:
P = V^2 / R
Where:
P is the power
V is the voltage
R is the resistance
Given:
Voltage (V) = 220 V
Resistance (R) = 12 Ω
P = (220 V)^2 / 12 Ω
P = 48400 J / 12 Ω
P = 4033.33 W
Calculating the Time Required
To calculate the time required to raise the temperature of the water, we can use the formula:
Q = P * t
Rearranging the formula, we can solve for time (t):
t = Q / P
t = 10,396,400 J / 4033.33 W
t ≈ 2575.23 seconds
Therefore, it would take approximately 2575.23 seconds to raise the temperature of 40 kg of water from 15°C to 80°C when using an electric heater with a resistance of 12 Ω and operated from a 220 V power line.
To determine the amount of heat required to raise the temperature of the water, we can use the specific heat capacity formula:
Q = m * c * ΔT
Where:
Q is the amount of heat energy
m is the mass of the water
c is the specific heat capacity of water
ΔT is the change in temperature
Calculating the Mass of Water
Given:
Mass of water (m) = 40 kg
Calculating the Specific Heat Capacity of Water
The specific heat capacity of water is approximately 4.186 J/g°C.
Calculating the Change in Temperature
The change in temperature (ΔT) is the difference between the final temperature and the initial temperature.
Given:
Initial temperature = 15°C
Final temperature = 80°C
ΔT = 80°C - 15°C = 65°C
Calculating the Amount of Heat Required
Using the values we have gathered, we can now calculate the amount of heat required to raise the temperature of the water.
Q = m * c * ΔT
Q = 40 kg * 4.186 J/g°C * 65°C
However, we need to convert the units of mass from kg to grams and the specific heat capacity from J/g°C to J/°C.
1 kg = 1000 g
1 J/g°C = 1 J/g°C * 1000 g/kg = 1000 J/°C
Q = 40,000 g * 4.186 J/°C * 65°C
Q = 10,396,400 J
Calculating the Power of the Electric Heater
The power (P) of an electric heater can be calculated using the formula:
P = V^2 / R
Where:
P is the power
V is the voltage
R is the resistance
Given:
Voltage (V) = 220 V
Resistance (R) = 12 Ω
P = (220 V)^2 / 12 Ω
P = 48400 J / 12 Ω
P = 4033.33 W
Calculating the Time Required
To calculate the time required to raise the temperature of the water, we can use the formula:
Q = P * t
Rearranging the formula, we can solve for time (t):
t = Q / P
t = 10,396,400 J / 4033.33 W
t ≈ 2575.23 seconds
Therefore, it would take approximately 2575.23 seconds to raise the temperature of 40 kg of water from 15°C to 80°C when using an electric heater with a resistance of 12 Ω and operated from a 220 V power line.
Community Answer
An electric heater has a resistance of 12 ohm and is operated from a 2...
Specific heat capacity of water is 4.2J/g/C hence the heat energy required is 40000*(80-15)*4.2 i.e 10920000
Heat released by the heater is V^2/R *T(time)
Thus make an equation out of the information-
48400/12*T = 10920000
Thus t comes out to be 2707 seconds(approximately)
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An electric heater has a resistance of 12 ohm and is operated from a 220 V power line. If no heat escapes from it, how much time is required to raise the temperature of 40 kg of water from 15 degree Celsius to 80 degree Celsius?
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An electric heater has a resistance of 12 ohm and is operated from a 220 V power line. If no heat escapes from it, how much time is required to raise the temperature of 40 kg of water from 15 degree Celsius to 80 degree Celsius? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An electric heater has a resistance of 12 ohm and is operated from a 220 V power line. If no heat escapes from it, how much time is required to raise the temperature of 40 kg of water from 15 degree Celsius to 80 degree Celsius? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electric heater has a resistance of 12 ohm and is operated from a 220 V power line. If no heat escapes from it, how much time is required to raise the temperature of 40 kg of water from 15 degree Celsius to 80 degree Celsius?.
An electric heater has a resistance of 12 ohm and is operated from a 220 V power line. If no heat escapes from it, how much time is required to raise the temperature of 40 kg of water from 15 degree Celsius to 80 degree Celsius? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An electric heater has a resistance of 12 ohm and is operated from a 220 V power line. If no heat escapes from it, how much time is required to raise the temperature of 40 kg of water from 15 degree Celsius to 80 degree Celsius? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electric heater has a resistance of 12 ohm and is operated from a 220 V power line. If no heat escapes from it, how much time is required to raise the temperature of 40 kg of water from 15 degree Celsius to 80 degree Celsius?.
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