A Shiny electric kettle with a 2.0kw heating element has a thermal capacity of 400j/k. 1kg of water at 20degrees celsius is placed in the kettle. The kettle is then switched on and 0.5kg of water remain after 13mins. Ignoring heat loss, calculate the value of specific heat of evaporation

To calculate the specific heat of evaporation, we need to determine the heat energy absorbed by the water and divide it by the mass of the water that has evaporated.

Step 1: Calculate the heat energy supplied by the kettle.
The formula to calculate heat energy is Q = mcΔT, where
Q = heat energy
m = mass
c = specific heat capacity
ΔT = change in temperature

Since the water is heated from 20°C to boiling point (100°C), the change in temperature is 100 - 20 = 80°C.

Using the given thermal capacity of 400 J/K and the time of 13 minutes (or 780 seconds), we can calculate the heat energy supplied by the kettle as follows:
Q = (thermal capacity) x (time)
Q = 400 J/K x 780 s
Q = 312,000 J

Step 2: Calculate the mass of water evaporated.
Since the initial mass is 1 kg and the final mass is 0.5 kg, the mass of water evaporated is:
Mass evaporated = initial mass - final mass
Mass evaporated = 1 kg - 0.5 kg
Mass evaporated = 0.5 kg

Step 3: Calculate the specific heat of evaporation.
The formula to calculate the specific heat of evaporation is given by Q = mL, where
Q = heat energy
m = mass evaporated
L = specific heat of evaporation

Using the calculated values from Step 1 and Step 2, we can rearrange the formula to solve for L:
L = Q / m
L = 312,000 J / 0.5 kg
L = 624,000 J/kg

Therefore, the specific heat of evaporation is 624,000 J/kg.

To calculate the specific heat of evaporation, we need to consider the energy required to heat the water from its initial temperature to its boiling point, and then the additional energy required to change its state from liquid to vapor.

Let's break it down step by step:

1. Calculate the energy required to heat the water from 20 degrees Celsius to its boiling point:
The formula for calculating the heat energy is Q = mcΔT, where:
Q = Heat energy (in Joules)
m = Mass of the substance (in kilograms)
c = Specific heat capacity (in J/kg·°C)
ΔT = Change in temperature (in °C)

In this case, the mass of water is 1 kg, the specific heat capacity is 400 J/kg·°C, and the change in temperature is the boiling point of water (100 °C) minus the initial temperature (20 °C).
Plugging in the values: Q1 = (1 kg) x (400 J/kg·°C) x (100 °C - 20 °C)

2. Calculate the energy required for evaporation:
To convert the remaining water (0.5 kg) into steam, we need to calculate the energy required to vaporize it. The formula for calculating heat energy during a phase change (such as evaporation) is Q = mL, where:
Q = Heat energy (in Joules)
m = Mass of the substance (in kilograms)
L = Latent heat of vaporization (in J/kg)

In this case, the mass of water is 0.5 kg, and we are looking for L, the latent heat of vaporization (specific heat of evaporation).

To find L, we can use the fact that when water reaches its boiling point, the heat energy gained during the heating phase equals the energy required for evaporation:
Q1 = Q2
(1 kg) x (400 J/kg·°C) x (100 °C - 20 °C) = (0.5 kg) x L
L = ((1 kg) x (400 J/kg·°C) x (100 °C - 20 °C)) / (0.5 kg)

Calculate the value of specific heat of evaporation by evaluating the expression above.

2KW is 7200 kJ in one hour.

So how much does it take to raise temperature of the kettle to 100 C.
400 x (Tfinal-Tinitial) = ?
How much to heat 1000 g H2O from 20 to 100.
q in kJ = 1 kg x 4.18 x (Tfinal-Tinitial) = ?
Add heat capacity q to q to raise 1000 g H2O to find total heat required to raise kettle and water to boiling.
How much heat do you have in that 13 min.
7200 x 13/60 = ? kJ
How much heat is left after getting H2O to the boiling point. That's
total J in 13 min - heat needed to raise kettle and water to 100 C = ?
Then heat vaporization x 500 g = heat left to boil water. The value in text is 40.65/mol. This is close to that but about 8% high.