an heating coil of R=100ohm is connected to 220v supply. calculate time taken if the coil heats 1kg of water from 25degree Celsius to 50degree Celsius
heat= electrical power
masswater*cwater*(50-25)=220^2/100 * timeinseconds
solve for time in seconds
To calculate the time taken for the heating coil to heat 1kg of water from 25 degrees Celsius to 50 degrees Celsius, we can use the formula:
Q = mcΔT
Where:
Q is the amount of heat energy required to raise the temperature of the water (in Joules),
m is the mass of the water (in kilograms),
c is the specific heat capacity of water (which is approximately 4.18 J/g°C for liquid water), and
ΔT is the change in temperature (in degrees Celsius).
Let's calculate the values first:
m = 1kg
c = 4.18 J/g°C
ΔT = 50°C - 25°C = 25°C
Now, we have all the values we need to calculate the amount of heat energy required to heat the water:
Q = (m) × (c) × (ΔT)
Q = 1kg × 4.18 J/g°C × 25°C
Q = 104.5 kJ (1 kJ = 1000 J)
Next, we need to calculate the time taken using the formula:
P = IV
Where:
P is the power consumed by the heating coil (in Watts),
I is the current flowing through the coil (in Amperes), and
V is the voltage across the coil (in Volts).
First, let's calculate the current:
I = V / R
I = 220V / 100Ω
I = 2.2A
Now, we can calculate the power:
P = IV
P = 2.2A × 220V
P = 484W (1 kW = 1000W)
To find the time, we can use the formula:
t = Q / P
t = 104.5 kJ / 484W
t ≈ 215.70 seconds
Therefore, it would take approximately 215.70 seconds (or about 3.59 minutes) for the heating coil to heat 1kg of water from 25 degrees Celsius to 50 degrees Celsius.