container holding 340g of water (initially at 14 degrees celsius) is placed in microwave oven, which is turned on for 3 minutes. Assuming all microwave energy is absorbed by water, how much water is left in container?
It would be helpful to know the radiation power of the microwave.
1000W
The microwave oven gives Q = P•t = 1000•180 =1.8•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 = 1.8•10^5 - 1.22•10^5 =
= 0.58•10^5 J.
This amount of heat transforms the mass m2 to the vapor
Q2 = r•m2 =2250000•m2,
m2 = 0.58•10^5/2250000 =2.58•10^-2 kg =0.0258 kg.
Mass of left water is m1-m2= 0.340-0.0258 =0.31422 kg
To determine how much water is left in the container after being in the microwave oven, we can use the concept of specific heat capacity. The specific heat capacity of water is 4.18 J/g°C, which means it takes 4.18 Joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius.
First, we need to calculate the amount of energy absorbed by the water in the microwave. To do this, we'll use the formula:
Energy (J) = mass (g) × specific heat capacity (J/g°C) × temperature change (°C)
Given:
Initial mass of water = 340g
Initial temperature of water = 14°C
Final temperature of water = Unknown (let's call it T)
We know that the temperature change is the final temperature minus the initial temperature:
Temperature change (°C) = T - 14
Now, let's calculate the energy absorbed by the water. Since the microwave is turned on for 3 minutes, we'll convert it to seconds:
Time (s) = 3 minutes × 60 seconds/minute = 180 seconds
Energy (J) = mass (g) × specific heat capacity (J/g°C) × temperature change (°C)
Energy (J) = 340g × 4.18 J/g°C × (T - 14)°C
The energy absorbed by the water is equal to the energy generated by the microwave. We'll assume that all the microwave energy is absorbed by the water.
Next, we need to consider the amount of energy generated by the microwave, which can vary depending on the microwave's power rating. Let's assume it has a power rating of P watts.
Energy (J) = Power (W) × Time (s)
Energy (J) = P watts × 180 seconds
Now we'll equate the two energy equations:
P watts × 180 seconds = 340g × 4.18 J/g°C × (T - 14)°C
Using this equation, you can plug in a specific power rating for the microwave to solve for the final temperature of the water. Once you know the final temperature, you can determine how much water is left in the container by utilizing the principle of conservation of mass.