If the time taken to melt 10g of ice at 0 degree Celsius is 1 minute, how long will it take to vaporize 10g of water at 100 degree celsius using the same heater? Pls show the solution clearly. Thanks
The amount of heat generated in 1 minute is 10 g*80 cal/g = 800 cal
You need 10*540 = 5400 calories to vaporize the same mass of water, at 100 C.
At the same heating rate as before, it will take 540/80 = 6.75 times longer to vaporize, or 6.75 minutes.
Physics - drwls, Thursday, November 15, 2012 at 6:13am
The amount of heat generated in 1 minute is 10 g*80 cal/g = 800 cal
You need 10*540 = 5400 calories to vaporize the same mass of water, at 100 C.
At the same heating rate as before, it will take 540/80 = 6.75 times longer to vaporize, or 6.75 minutes.
To solve this problem, we need to calculate the amount of heat required to vaporize 10g of water at 100 degrees Celsius.
The heat required to change the temperature of a substance without phase change can be calculated using the specific heat formula:
Q = mcΔT
Where:
Q is the heat energy
m is the mass of the substance
c is the specific heat capacity
ΔT is the change in temperature
For water, the specific heat capacity (c) is approximately 4.18 J/g°C.
First, we need to find the amount of heat required to raise the temperature of 10g of water from 0°C to 100°C:
Q1 = (10g) * (4.18 J/g°C) * (100°C - 0°C)
Q1 = 4180 J
Now, to vaporize the water, we need to consider the heat of vaporization. The heat of vaporization (also known as latent heat) for water is approximately 2260 J/g.
The amount of heat required to vaporize 10g of water can be calculated as:
Q2 = (10g) * (2260 J/g)
Q2 = 22600 J
Finally, to find the total amount of heat required to vaporize the water, we add up Q1 and Q2:
Qtot = Q1 + Q2
Qtot = 4180 J + 22600 J
Qtot = 26780 J
Now, we can calculate the time required to provide this amount of heat using the power rating of the heater. Let's assume the heater has a power rating of 1000 watts (W).
The formula to calculate the time (t) required is:
Qtot = P * t
Where:
Qtot is the total amount of heat
P is the power rating of the heater
t is the time
Substituting the known values, we have:
26780 J = (1000 W) * t
Solving for t:
t = 26780 J / 1000 W
t ≈ 26.78 seconds
Therefore, it will take approximately 26.78 seconds to vaporize 10g of water at 100 degrees Celsius using the same heater.