# An object with a mass of #4 kg#, temperature of #240 ^oC#, and a specific heat of #15 J/(kg*K)# is dropped into a container with #15L # of water at #0^oC #. Does the water evaporate? If not, by how much does the water's temperature change?

The object does not vaporise the water. It causes a temperature change of

Evaporation of a liquid can occur at any temperature. So we could say "Yes" in answer to the question "Does the water evaporate?" However, let’s assume the question meant "Does all of the water get vaporised?" (I.e. is the water raised to its boiling point and then boiled away?)

To answer the question I will structure my solution as follows:

Some preliminary data and calculations.

Conversion of the volume of water into m³:

Calculation of the mass of water:

Specific heat capacity of water:

Latent heat of vaporisation of water:

An initial note about the question.

The provided data indicates that the object has a smaller mass and a much lower specific heat capacity than water.

Thus, it appears that the object will have a very small impact on the water, so small in fact that I wonder if some of the data that was provided was inaccurate.

- The amount of energy needed to raise water's temperature to boiling.

- The amount of energy needed to evaporate all the water.

- Energy that the 4 kg object can provide.

It is not even necessary to compare 8400 J with the energy needed to evaporate the water (which was determined in part 2).

- How much does the temperature of the water change?

We just need to apply the specific heat capacity equation for the object and the water because we already know that the latter does not go through a phase change.

We can say the following if we assume that the water absorbs all of the heat energy that the object transfers:

Taking note of the temperature variations mentioned above, we can further define the terms ∆θ:

Replace those with those in equation ①:

Now enter the values into the formula:

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To determine if the water evaporates, we need additional information, such as the latent heat of vaporization. Assuming no evaporation, the water's temperature increases by approximately 10.67 degrees Celsius.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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