Question

Part I: Choose five of these questions. (12 points each) 1. Here is the van der Waals Equation for one mole of gas P Given this equation, how does the infinitesimal change in pressure, or as specific as possible. (In other words, evaluate the derivatives.) with d V and dT? B e-NV, where is the sity her of molecules and V is the fshe wall perpendicular to the 2. A sample of gas molecules of density N e e N is the numbe volume) is moving with a speed in the direction. The area of the unple will make with Les that this axis is A. Given this information what is the number of collisions full credit, do not just the wall in time, At? Please explain the reason behind what you write down the final answer! 3. Consider a sample of hydrogen gas and ammoniagas volume and temperature. Why does it make sense that under these con same compressibility even though these are very different gases? Are compressible under these conditions than if they were ideal con gas and amcaseachas held at its own critical pressure, these conditions they would have the on these are very different gases? Are these gases more or less conditions than if they were al? How do you know? (Explain.) 4. Verify that the root mean square speed is 3RT here M is the molar mass, T is the absolute temperature and R is the gas constante the Maxwell-Boltzmann distribution ven herefW= of molecular speeds. It is given here: f(x) = 45 ve 3. In class, we used data to obtain the following cut for compressibility of water at 373 K: z(p) - 1 - (5.16 x 10' p + (1.07 x 105 (p has units of bar here.) Would water vapor behave ideally at 100 bar? If not, is it more or less compressible? If it is not ideal, explain any deviations from ideality for water vaporat 100 bar. What is happening with the molecules? What is the molar volume of water vaporat 100 bur? 6. An ideal gas undergoes an isothermal reversible expansion from P to P. The same gas, starting at the same conditions, undergoes an adiabatic reversible expansion from P to P. Compare these two processes. How do the work, heat, AT, V and AU compare? Don't do any calculations This question is about the explanation 7. Why is Cp is greater than Cy for gases? (Explain) A gas is heated at constant pressure. What is the sign of AH? Does AU equal AH for this process? If you answer is yes, explain. If your answer is to say how their values would differ, and why. Please refer to the first law as part of your explanation 9. For an adiabatic an adiabatic, reversible expansion, derive the following equation relating the final temperature e initial temperature and the initial and final pressures. Justify your steps, and make any needed mptions. You should start with the differential form of the First Law of Thermodynamics. In T, -InT- P

1,4?

Answer 1

SOLN 1

(a) First evaluating dP/dv ' () ਸੰਦੇ, ਚ ਨੇ, ( PM _2a_RT . (b) Now evaluating de/dT ਸ, ਰੰਜਸ਼ ਹੈ, ਬੰਗਾ )-ਰਸ) ੭.੬)

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