a large container holding 340g of water, initially 14°C is placed in a microwave oven. the magnetron in the microwave oven can produce 900W of electromagnetic radiation. the microwave is turned on for 3 minutes. assuming all microwave energy is absorbed by the water, how much water is left in the container?

The microwave oven gives Q = P•t = 900•180 =1.62•10^5 J.

The amount of heat necessary to heat the water to 100oC
Q1 = c•m1•Δt = 4180•0.340•86 = 1.22•10^5 J,
Q2 = Q – Q1 = 1.62•10^5 - 1.22•10^5 = 0.4•10^5 J.
This amount of heat transforms the mass m2 to the vapor
Q2 = r•m2 =2250000•m2,
m2 = 0.4•10^5/2250000 =1.78•10^-2 kg =0.0178 kg.
Mass of left water is m1-m2= 0.340-0.0178 =0.322 kg

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To calculate how much water is left in the container after it is heated in the microwave oven, we need to understand the concept of specific heat capacity and use the formula for calculating the amount of heat absorbed or released by a substance.

The formula to calculate the amount of heat absorbed or released by a substance is given by:

Q = m * c * ΔT

Where:
- Q is the amount of heat absorbed or released (in Joules).
- m is the mass of the substance (in grams).
- c is the specific heat capacity of the substance (in J/g°C).
- ΔT is the change in temperature (in °C).

First, let's calculate the amount of heat absorbed by the water using the formula:

Q = m * c * ΔT

Given:
m = 340g (mass of water)
c = 4.18 J/g°C (specific heat capacity of water)
ΔT = final temperature - initial temperature
= ? - 14°C

Since there is no information about the final temperature, we need to make an assumption. Let's assume that the water gets heated to its boiling point, which is 100°C.

ΔT = 100°C - 14°C
= 86°C

Now, we can calculate the amount of heat absorbed by the water:

Q = m * c * ΔT
= 340g * 4.18 J/g°C * 86°C

Calculating this, we get:

Q = 124,334.8 J

The next step is to calculate the amount of energy supplied by the microwave oven. We are given that the magnetron in the microwave oven can produce 900W of electromagnetic radiation and the microwave is turned on for 3 minutes.

To convert the time from minutes to seconds, we multiply it by 60:

Time in seconds = 3 minutes * 60 seconds/minute
= 180 seconds

Now, we can calculate the total energy supplied:

Energy supplied = Power * Time
= 900W * 180 seconds
= 162,000 J

Given that all the microwave energy is absorbed by the water, we can equate the energy supplied to the amount of heat absorbed:

162,000 J = 124,334.8 J + energy used to heat container

To calculate the energy used to heat the container, we need to consider that some heat is lost to the surroundings. Let's assume that 10% of the energy used to heat the container is lost.

Energy used to heat container = 0.10 * 124,334.8 J
= 12,433.48 J

Now, we can subtract the energy used to heat the container from the total energy supplied:

Energy supplied - energy used to heat container = 162,000 J - 12,433.48 J
= 149,566.52 J

Therefore, the total energy used to heat the water is 149,566.52 J.

Finally, to determine how much water is left in the container, we need to calculate the mass of the water remaining. We can rearrange the formula to solve for mass:

Q = m * c * ΔT

m = Q / (c * ΔT)
= 149,566.52 J / (4.18 J/g°C * 86°C)

Calculating this, we get:

m = 42.57 g

Therefore, approximately 42.57 grams of water are left in the container after being heated in the microwave oven.