26. An electric kettle with negligible heat capacity is
rated at 2000 W. If 2.0kg of water is put in it,
how long will it take the temperature of water to
rise from 200C to 1000C?
A. 420s
B. 336s
C. 168s
D. 84s.
To find the time it takes for the temperature to rise from 20°C to 100°C, we can use the formula:
Q = mcΔT
Where:
Q = heat transferred
m = mass of water
c = specific heat capacity of water
ΔT = change in temperature
The specific heat capacity of water is approximately 4.18 J/g°C.
First, we need to convert the mass of water from kg to grams:
2.0kg * 1000g/kg = 2000g
Next, we calculate the heat transferred:
Q = (2000g)(4.18 J/g°C)(80°C)
Q = 668,800 J
Now, we use the formula for power:
P = Q/t
Where:
P = power (in watts)
Q = heat transferred (in joules)
t = time (in seconds)
We rearrange the formula to solve for time:
t = Q/P
t = 668,800 J / 2000 W
t = 334.4 s
So, it will take approximately 334.4 seconds for the temperature to rise from 20°C to 100°C.
Since none of the answer choices match exactly, we can round to the nearest whole number, which would be 334 seconds.
Therefore, the closest answer choice is B. 336s.
To find the time it takes for the temperature of the water to rise from 20°C to 100°C, we can use the equation:
Q = m * c * ΔT
Where:
Q is the heat transferred
m is the mass of the water
c is the specific heat capacity of water
ΔT is the change in temperature
First, we need to find the heat transferred. The equation for heat transferred is:
Q = P * t
Where:
P is the power of the kettle
t is the time taken
Given that the power of the kettle is 2000 W, we can write:
Q = 2000 * t
Next, we need to find the change in temperature. We subtract the initial temperature from the final temperature:
ΔT = 100°C - 20°C
ΔT = 80°C
We know that the mass of the water is 2.0 kg and the specific heat capacity of water is approximately 4.18 J/g°C. We can convert the mass to grams by multiplying by 1000:
m = 2.0 kg * 1000 g/kg
m = 2000 g
Now we can substitute these values into the equation for Q:
2000 * t = m * c * ΔT
2000 * t = 2000 g * 4.18 J/g°C * 80°C
Simplifying:
t = (2000 g * 4.18 J/g°C * 80°C) / 2000
t = 334.4 s
Rounding to the nearest whole number, the time it will take for the temperature of the water to rise from 20°C to 100°C is approximately 334 seconds.
Therefore, the closest option to the correct answer is B. 336s.