3. [-/21 Points] DETAILS MY NOTES A gas expands from / to F along the three paths indicated in the figure below. Calculate the work done on the gas along each of the following paths. (1 L. atm = 101.325 / ) P(atm) 10 1 2 B. V (liters) BIAF J (1) (b) IF J (+) (C) IBF (1) Submit Answer 4. [-/37 Points] DETAILS MY NOTE Three moles of gas initially at a pressure of 2.00 atm and a volume of 0.300 L has internal energy equal to 91.0 J. In its final state, the gas is at a pressure of 1.50 atm and a volume of 0.800 L, and its internal energy equals 182 J. P (atm) 2.00 1.50 - 0.300 0,800 V (liters) (a) For the paths IAF, IBF, and IF in the figure above, calculate the work done on the gas. WIAF WIBF WIF (b) For the paths JAF, IBF, and IF in the figure above, calculate the net energy transferred to the gas by heat in the process. QIAF Q IBF 1I (2) QIF= ( # ) This question does not support 'Practice another Version'5. [-/14 Points] DETAILS MY NOTE Pressure (Fa) 30 50 10 - 30 Volume [m*3) 3 5 6 7 8 9 10 Consider the pressure vs. volume graph above. This is a plot of a pressure function of the form P = (8 Pa) + (5 Pa/m ). V + (0.04 Pa/m6)-v2 + 11 Pa.m] V What is the work done by the system as the volume changes from 5 m to 8 m? (4) What is the work done by the system as the volume changes from & m to 5 m? (4 ) It is very difficult to estimate the area to 3 significant figures by graphical methods. However, a computer program can apply those methods to many small sections and obtain an area that is accurate enough. Use this GlowScript program to calculate the area under the pressure vs volume curve. Modify the program below to match the specifics of this question: "Change the first and last volumes from first = 1 and last = 20 to first = 5 and last = 8. "Change the coefficients in the formula function (co, c1, c2, and c3) to match the values above ( 8, 5, 0.04, and 11). " Adjust the number of trapezoid pieces (change the value of n) to get 3 significant figure consistency in the area. Suggestion: start with n = 20, and double that value on each consecutive execution (40, 80, 160. ..) until the previous and current values agree to 3 sig. figs. For many web browsers the program is shown below, if not shown then it is available at this link. trinket * Plans Learn Help Sign Up Log In1. [-/13.4 Points] DETAILS MY NOTES ner function for thermal physics. There is a set of 18 coins. We want to select & coins from that set. The nor function gives us the number of ways to obtain 8 items from a total of 18 items. What is ncr(18, 8)? ncr(18, 8) - What is nCr(18, 10)? ncr(18, 10) = From probability, we have the nor function (also called the combination function) which lets us calculate the number of ways we can select & items from a set of 18. This function is valid for the case where we do not care which order the items are selected and we do not replace the selected item before the following selections. The arguments to the nor function are non- negative integers. There are several notations for this function such as ncr( n, k), C," , and n Ck, and it is also called the binomial coefficient. The ner function can be calculated using the factorial function: Ck = ncr(n, k) = n! ki(n-k) However, nearly all scientific calculators have the nor function built in and the built-in function is usually faster and can handle larger numbers than the calculation using the factorial function. Spreadsheets have the nor function which is called COMBIN "=COMBIN( Ntotal, Nselected)" Why use the ner function? We use the nor function in thermal physics to determine the number of ways a particular state can be obtained. We simplify our study by using simple systems made up of items that can be in one of two states, such as coins which can be "head" or "tail". If we have 18, the number of ways we can obtain 8 coins with "heads" and -8 tails is given by the nor function. For example for 10 coins, there are 210 ways we could get 5 heads and 5 tails. ncr( 10, 5) - 252 In thermal physics we use yet another notation and call the number of combinations the "multiplicity" of a macrostate. We can relate the probability of having 6 heads out of 10 coins to the entropy of the macrostate with 5 heads out of 10 coins. The multiplicity of 6 heads out of 10 coins can be written as $2(6,5), which is read as the multiplicity of the state with 6 heads and 5 tails. We use the ner function to calculate the multiplicity: 0( 6, 4) - nCr( 10, 6) = 210 We can also calculate the number of ways the coins can be arranged, which is the sum of the multiplicities for all possible number of heads: Qtall) - 2 Number of coins - 210 s - k, In(ncr(Number of coins ) - k. InCAG.)) Where ka - 1.38065 x 10-23 _ (Note: In a lab exercise, we may choose a units system that makes k, have the value of one, to simplify the repeated calculations.) Many calculators have a function called nor which calculates the multiplicity: Jsing 200 nCr 100 ( # 9.05485146561033 x 10 jas an example: For TI-30%: 200; press "PRD" key: press D key: press "ENTER/"; 100; press "ENTER/-". For TI-84: 200; press "Math" key; press