A dilute gas expands quasi-statically from 0.45 to 4.2 L at a constant temperature of 310 K. Follow the steps below to c

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A Dilute Gas Expands Quasi Statically From 0 45 To 4 2 L At A Constant Temperature Of 310 K Follow The Steps Below To C 1 (145.31 KiB) Viewed 54 times

A Dilute Gas Expands Quasi Statically From 0 45 To 4 2 L At A Constant Temperature Of 310 K Follow The Steps Below To C 2 (102.41 KiB) Viewed 54 times

A dilute gas expands quasi-statically from 0.45 to 4.2 L at a constant temperature of 310 K. Follow the steps below to calculate the number of molecules in the gas, with some additional information provided. Hint a. For an isothermal expansion, does the pressure of the gas remain constant? Hint for (a) Answer depends on additional information not given. Yes, it remains constant. O No, it does not remain constant. b. If the pressure does not remain constant, we cannot calculate the whole amount of work with W = PAV. Instead, we need to start out with the infinitesimal work done for infinitesimal volume change (dW = PdV) and integrate over the interval of volume change to calculate the total work done (this is also same as the area under the curve in P-V diagram). Fill in the blank in the setup for the integral below, in terms of V (volume), N (number of molecules), T (temperature), and k (Boltzmann constant) and other numerical constants. Hint for (b) Total work done in volume change from V₂ to Vƒ is, - S dV. W = V₁ NKT V
c. Complete the integral above and write down work done in terms of V₁, Vƒ, N, T, k, and other numerical constants. Hint for (c) Total work done in volume change from V₂ to Vf is, -8 W = 2.86 107 X (Format hint: Subscripts are typed using underscores. For example, to type V₁, type in "V_i". Natural logs are represented with function "ln". That is, for "natural log of 12", for example, type in "ln(12)".) N d. Suppose that amount of 335 J of work was done in this expansion. Find the value of N (that is, how many molecules are in this gas?). Hint for (d) = 3.715E22 X (Format Hint: Use the "E" notation to enter numbers in scientific notation. For example, 3.14 × 10¹² can be written as "3.14E12".)