Background

In thermodynamics, we are often interested in knowing how much space a fluid take up$,$ which we specify using the fluid's volume. The fluid volume is useful, but it turns out that a more useful thermodynamic property is the volume per$-$unit$-$mass, or the specific volume

$.$ Note that the specific volume is just the inverse of the more$-$familiar density. The specific volume of single$-$phase fluids $($e$.$g$.,$ steam$)$ is just something you can look up in a table. The specific volume of a liquid$-$vapor mixture, however, depends on the fractions$$of liquid and vapor in the mixture. The mass fraction of vapor to total fluid is called the quality

$$of the fluid. The quality of a liquid$-$vapor mixture can range from $0$ for a pure liquid to $1$ for a pure vapor $.$ Using the quality, we can calculate the average specific volume of a so$-$called saturated liquid$-$vapor mixture$$as

where $$and $$are the specific volumes of the liquid and vapor parts of the mixture, respectively. The second equals sign introduces the common shorthand $.$

The specific volumes of the vapor $$and liquid $$parts of the mixture depend on the mixture's temperature and pressure and the type of fluid. Here, you will only account for the differences in fluid.

Your Task

Write a function called SpecificVolume$$that calculates the specific volume of a liquid$-$vapor mixture given its quality $$and the type of fluid $($water or R$-134$a

$).$ Your function will take a single input and return a single output.

The input will be a $[$m x $2]$ vector where the first column represents the quality of a saturated mixture and the second column represents the substance $($either $0$ for water or $1$ for R$-134$a$).$

The output will be a $[$m x $1]$ column vector of the calculated specific volumes. Each row of your output should correspond to the same row of the input.

The specific volumes of the liquid and vapor parts of the mixture for water and R$-134$a are:

Please make sure to use all the provided digits when writing your code. If you round or otherwise cut off digits, it is likely your solution will be marked as incorrect.

Guidance$/$Hints

Use a for loop to evaluate $$for each row of the function input. To do this, you will need to nest a conditional statement inside your for loop that determines whether the substance is water or R$-134$a$.$ You can then use the appropriate specific volume values to calculate $.$

You will need to use array indexing

$$to both call and store the appropriate elements of relevant arrays.

Don't forget to preallocate the size of your output before the for loop.

Final Notes

I know that not all of you have taken thermodynamics. Please note, however, that this is fundamentally just a math problem and you do not need any knoweldge of thermodynamics to complete it$.$ Thermodynamics is simply an interesting$/$useful lens through which to view this math problem, given that most of you are mechanical and aerospace engineers and you will study thermodynamics in appreciable depth during the next couple of years. Background

In thermodynamics, we are often interested in knowing how much space a fluid take up$,$ which we specify using the fluid's volume. The fluid volume is useful, but it turns out that a more useful thermodynamic property is the volume per$-$unit$-$mass, or the specific volume $(\backslash ($ v $\backslash )).$ Note that the specific volume is just the inverse of the more$-$familiar density. The specific volume of single$-$phase fluids $($e$.$g$.,$ steam$)$ is just something you can look up in a table. The specific volume of a liquid$-$vapor mixture, however, depends on the fractions of liquid and vapor in the mixture. The mass fraction of vapor to total fluid is called the quality $\backslash (($x$)\backslash )$ of the fluid. The quality of a liquid$-$vapor mixture can range from $0$ for a pure liquid to $1$ for a pure vapor $\backslash ((0$