Physics, 31.12.2019 02:31 samueladetoro54

Given the temperature and mass as input variables, construct a spreadsheet that uses linear interpolation to determine hv and the pressure and then calculate the required amount of heat to completely vaporize the water.

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Answer from: maxB0846

Hi. I think that you must specify that both temperature and pressure are at saturation point. I'm attaching a document and I hope it provide enough information in order to understand clearly the explanation below

Explanation:

In order to give a solution to this problem you should take into account the following steps:

Type the following properties: Saturation temperature, saturation pressure, enthalpy of saturated liquid (hf) and enthalpy of saturated vapour (hg). I personally suggest the annexed properties tables of Yunes Cengel.Extract the necessary data in order to calculate the unknown properties (pressure and hv). This part is really important because we have to use specific commands in the spreadsheet; I'm going to explain it deeply below:First of all, we must provide a temperature and we have to extract from the properties table in the spreadsheet: the nearest lower temperature and the nearest higher temperatureTo do this, we must use the command lookup. The task of this command is search a value close to a value provided. The command lookup always extract the nearest lower value.

The command lookup is used like this:

=+lookup(Value provided by the user; list to compare the value provided; corresponding data list)

In this case, the value provided by the user is any temperature, the list to compare the value provided is the column of saturating temperature and the corresponding data list is the saturating pressure (or the enthalpy)

Now, we have to extract the nearest higher value. To do this, we must take into account that the nearest higher value correspond to the value located in the next row of the nearest lower valueIf we know the arrow where a value is located, we can use the command index and we can extract its value.

The comand index is used like this:

=index(data matrix, row, column)

In this case the data matrix is the properties table that you type in the spreadsheet, row is the row where is located the nearest lower value (since we are extracting the nearest higher value you must type row +1) and column is the column of interest data (in this case the pressure or the enthalpy).

Once you extract all the information that you need the following step is to interpolate with equation (1):

(1) $y=y_0+\frac{y_1-y_0}{x_1-x_0}*(x-x_0)$

Remember that y is the dependent variable (in this case, pressure or enthalpy) and x is the independent variable (in this case, temperature)

Finally, calculate the amount of heat to vaporize any quantity of water. To do this, you must multiply the interpolated value of vaporization enthalpy by the mass of water (in mass or moles according to the units). The equation is shown below:

(2) $Q=h_{vap}*Mass_{water}$

I know that understanding the commands is a bit complicated, for that reason I attached a spreadsheet with an example. I suggest to read the explanation and analyze carefully the commands.

Answer from: Quest

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Answer from: Quest

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Given the temperature and mass as input variables, construct a spreadsheet that uses linear interpol...

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