Problem: Write an article based on this summary: Cut some  4-inch lengths from #3 and #5 ribbon until you have enough to create cones around the entire edge of one cardboard backer. Overlap the pieces and twist both ends in the same direction to form a cone shape. Staple the completed cone-shaped ribbon to the back edges of the cardboard backer. Fill in the spaces between the cones with a second row of cones using the second color of ribbon. Remove the stem from the mum flower. Take the backer of the pointed ribbons and glue the mum to the front middle of the backer using a hot glue gun. Pick up #5 and #9 ribbon in the color of your choice and cut several 48-inch-long strips. Take your 48-inch pieces and fold them in half to create 24-inch streamers. Embellish the lengths of the ribbons with any sort of decorations you desire once your backer looks full of ribbons Some ideas includes writing words out in glitter glue, fastening beads, rhinestones, or small plush figurines, and even putting photographs on the ribbons. Make a military braid from your ribbons if desired. Tie on bells using curling ribbon if desired. Take two 5-inch pieces of #5 and #9 ribbon and overlap them several times to form a loop. Complete embellishments to your satisfaction. Glue any central charms on the mum and add any final touches to the piece. To wear your mum, take your large safety pin and thread it through the loop you created on the back backer with the two 5-inch pieces of ribbon. Finished!

Answer: Start with about 5 cuts of each color and cut more as needed. Make sure that every cone has the shiny side of the ribbon facing outward. Staple the ribbon on it's fold to hold the cone shape. Position the cones so that the points are pointing away from the backer, staple base of the cone. For the first layer, use the same color cones and leave about a quarter to a half inch of space between each cone. Continue to staple the cones until the entire edge of the backer is filled with cones. It should look like a drawing of a sun or a flower.    {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/b\/ba\/Make-Homecoming-Mums-Step-6Bullet1.jpg\/v4-460px-Make-Homecoming-Mums-Step-6Bullet1.jpg","bigUrl":"\/images\/thumb\/b\/ba\/Make-Homecoming-Mums-Step-6Bullet1.jpg\/aid466916-v4-728px-Make-Homecoming-Mums-Step-6Bullet1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"<div class=\"mw-parser-output\"><p>License: <a rel=\"nofollow\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"} Remember to staple  the base of the cone on the backside of the backer. The flower can be either real or fake, but most used are generally fake to prevent wilting. Set the mum aside and allow the glue to dry for several minutes. If you want to make a double mum, simply use a double backer with two holes instead of one and attach two flowers using a glue gun. Again, start with about 5 strips of each and then cut as many  as needed to create a full-looking mum.  Be sure to use a hot glue gun to fasten charms and other heavier objects to the ribbons. To make a military braid, begin by stapling the ends of two different colored ribbons together at a right angle.  Next, fold a colored ribbon towards you, forming a loop as long as the ribbon is wide and staple the ribbons together where they intersect. Take a loop of your second ribbon and bring it through the original loop of the first ribbon. Continue to bring a loop of the first ribbon through the second ribbon and pull the second ribbon tight around the first ribbon. Remember to alternate ribbon colors as you continue to do this until you reach the end of the ribbons. You will use your middle backer with the streamers for this step.  Cut several pieces of curling ribbon each 36 inches (91.4 cm) long and tie a small bell to the end of each piece. Attach to the middle backer using hot glue. Staple the loop to the top center of the third, unused backer. This will serve as the base for your safety pin. Glue the third backer with the safety pin loop onto the back of middle backer to cover staple edges and protect clothing from staple snags. Allow the glue to dry. Then simply attach the pin to your clothing.


Problem: Write an article based on this summary: Write the Clausius-Clapeyron equation. Plug in the variables you know. Plug in your constants. Solve the equation.

Answer:
The formula used for calculating vapor pressure given a change in the vapor pressure over time is known as the Clausius-Clapeyron equation (named for physicists Rudolf Clausius and Benoît Paul Émile Clapeyron). This is the formula you'll use to solve the most common sorts of vapor pressure problems you'll find in physics and chemistry classes. The formula looks like this: ln(P1/P2) = (ΔHvap/R)((1/T2) - (1/T1)). In this formula, the variables refer to:   ΔHvap: The enthalpy of vaporization of the liquid. This can usually be found in a table at the back of chemistry textbooks.  R: The real gas constant, or 8.314 J/(K × Mol).  T1: The temperature at which the vapor pressure is known (or the starting temperature.)  T2: The temperature at which the vapor pressure is to be found (or the final temperature.)  P1 and P2: The vapor pressures at the temperatures T1 and T2, respectively. The Clausius-Clapeyron equation looks tricky because it has so many different variables, but it's actually not very difficult when you have the right information. The most basic vapor pressure problems will give you two temperature values and a pressure value or two pressure values and a temperature value — once you have these, solving is a piece of cake.  For example, let's say that we're told that we have a container full of liquid at 295 K whose vapor pressure is 1 atmosphere (atm). Our question is: What is the vapor pressure at 393 K? We have two temperature values and a pressure, so we can solve for the other pressure value with the Clausius-Clapeyron equation. Plugging in our variables, we get ln(1/P2) = (ΔHvap/R)((1/393) - (1/295)). Note that, for Clausius-Clapeyron equations, you must always use Kelvin temperature values. You can use any pressure values as long as they are the same for both P1 and P2. The Clausius-Clapeyron equation contains two constants: R and ΔHvap. R is always equal to 8.314 J/(K × Mol). ΔHvap (the enthalpy of vaporization), however, depends on the substance whose vapor pressure you are examining. As noted above, you can usually find the ΔHvap values for a huge variety of substances in the back of chemistry or physics textbooks, or else online (like, for instance, here.)  In our example, let's say that our liquid is pure liquid water. If we look in a table of ΔHvap values, we can find that the ΔHvap is roughly 40.65 kJ/mol. Since our H value uses joules, rather than kilojoules, we can convert this to 40,650 J/mol.  Plugging our constants in to our equation, we get ln(1/P2) = (40,650/8.314)((1/393) - (1/295)). Once you have all of your variables in the equation plugged in except for the one you are solving for, proceed to solve the equation according to the rules of ordinary algebra.  The only difficult part of solving our equation (ln(1/P2) = (40,650/8.314)((1/393) - (1/295))) is dealing with the natural log (ln). To cancel out a natural log, simply use both sides of the equation as the exponent for the mathematical constant e. In other words, ln(x) = 2 → eln(x) = e2 → x = e2.  Now, let's solve our equation: ln(1/P2) = (40,650/8.314)((1/393) - (1/295)) ln(1/P2) = (4,889.34)(-0.00084) (1/P2) = e(-4.107)  1/P2 = 0.0165 P2 = 0.0165-1 = 60.76 atm. This makes sense — in a sealed container, increasing the temperature by almost 100 degrees (to almost 20 degrees over the boiling point of water) will create lots of vapor, increasing the pressure greatly