# Thermodynamics problem -- Find the mass of water that vaporizes

• Alice7979
In summary: The water will heat up to boiling temperature, then any additional energy will not raise the temperature (it instead goes into vaporization).
Alice7979

## Homework Statement

Find the mass of water that vaporizes when 3.02 kg of mercury at 223 °C is added to 0.347 kg of water at 83.4 °C.

## Homework Equations

Mercury Q = Water Q + Water mL
mc∆t= mc∆t + mL

## The Attempt at a Solution

mass of vapor = ((3.02)(140)(223-tfinal) - (4186)(.347)(change in temperature))/100

I don't know the change in temperatures for sure, all the ones i have tried are wrong.

Alice7979 said:
all the ones i have tried are wrong.
It’s not a guessing game! The water will heat up to boiling temperature, then any additional energy will not raise the temperature (it instead goes into vaporization).

Alice7979 said:
mc∆t= mc∆t + mL
This equation could solve the problem, if you have the correct subscripts (there are two c’s, two ∆t‘s, and three masses involved).

Alice7979 said:

## Homework Statement

Find the mass of water that vaporizes when 3.02 kg of mercury at 223 °C is added to 0.347 kg of water at 83.4 °C.

## Homework Equations

Mercury Q = Water Q + Water mL
mc∆t= mc∆t + mL

## The Attempt at a Solution

mass of vapor = ((3.02)(140)(223-tfinal) - (4186)(.347)(change in temperature))/100

I don't know the change in temperatures for sure, all the ones i have tried are wrong.
Although not state explicitly, this assumes that the water is in contact with air at 1 atm, so the evaporation takes place at 100 C (the final temperature).

Nathanael
Nathanael said:
It’s not a guessing game! The water will heat up to boiling temperature, then any additional energy will not raise the temperature (it instead goes into vaporization).This equation could solve the problem, if you have the correct subscripts (there are two c’s, two ∆t‘s, and three masses involved).

mass of vapor = ((3.02)(140)(223-100) - (4186)(.347)(100-92.8))/100 = 540.6

That's what i tried but i still get it wrong, is it the change in temperature i have wrong?

How much heat does the mercury give up in cooling from 223 to 100 C? How much of this heat must be used to heat the water up from 92.8 C to 100 C? The rest of the heat is used to vaporize some of the water.

Alice7979 said:
mass of vapor = ((3.02)(140)(223-100) - (4186)(.347)(100-92.8))/100 = 540.6

That's what i tried but i still get it wrong, is it the change in temperature i have wrong?
It would be nice, in the future, if you provided all relevant constants, so that I don’t have to look up everything.

It looks like you’re saying the energy of vaporization is 100 J/kg ?
Also I thought it started at 83.4 degrees not 92.8?

Nathanael said:
It would be nice, in the future, if you provided all relevant constants, so that I don’t have to look up everything.

It looks like you’re saying the energy of vaporization is 100 J/kg ?
Also I thought it started at 83.4 degrees not 92.8?
Yes, I did have that wrong but I found it. Thanks

## What is thermodynamics?

Thermodynamics is the branch of science that deals with the study of energy and its transformation in physical systems. It also involves the relationship between heat, work, and temperature.

## What is vaporization?

Vaporization is the process by which a liquid is converted into a gas or vapor. This occurs when the molecules in a liquid gain enough energy to break free from their attractive forces and escape into the gas phase.

## How do you find the mass of water that vaporizes?

In order to find the mass of water that vaporizes, you must first determine the change in energy during the phase transition from liquid to gas. This can be calculated using the enthalpy of vaporization, which is the amount of energy required to convert one unit of mass from liquid to gas at a constant pressure. Once the change in energy has been determined, you can use the specific heat capacity of water to calculate the mass that has vaporized.

## What factors affect the mass of water that vaporizes?

The mass of water that vaporizes is affected by several factors, including the temperature and pressure of the surroundings, the initial mass and temperature of the liquid water, and the specific heat capacity of water. In addition, the rate of vaporization can also be influenced by the surface area of the liquid and the presence of impurities.

## How is thermodynamics related to the mass of water that vaporizes?

Thermodynamics is directly related to the mass of water that vaporizes, as it involves the study of energy and its transformation during physical processes such as vaporization. By applying the laws of thermodynamics, we can accurately calculate the mass of water that will vaporize under certain conditions and make predictions about the behavior of this process.

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