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- Please solve d. When the system is at psi(x, 0), what is ⟨p(hat)2⟩?Question 2 Quickly estimate the change in enthalpy /mol) to go from CO2 at 325K and 1 bar to 298K and 97 bar. Hint: of. Figure 2.6c.A rubberized sphere contains carbon dioxide. If the initial radius of the sphere is 15cm: How much work is done if the carbon dioxide-filled sphere expanded to five times its original volume against the pressure at STP? Express your answer in L atm. b. Upon the expansion of the sphere, what is the kinetic energy of a single carbon dioxide molecule if it travels across the diameter and covers it in 30ms? Assume that the sphere contains one mole of carbon dioxide. Express your answer in J. How much power can all the molecules in this sphere generate after 30s? Assume that the sphere contains one mole of carbon dioxide and that all molecules have the same kinetic energy. Express your answer in W. (Use the KE obtained from the previous required) 2. A rubberized, cubic chamber was filled with butane gas and was expanded from 3.0L to 4.5L at a pressure of 2.7atm and it absorbed 230J of heat from the surroundings. a. What is the change in the energy of the system? Express your answer in L…
- define the chemical potential in terms of derivatives of the ĈE energy E and enthalpy H. For a one component system, these are u= ON and Evaluate these expressions for an ideal gas and compare to ON µ = -kT In (kT/PA³ ) from H=| P,s OF and |= 1 TP ON v.rQ /Find the next integral: E V 2m(E – %x)dx h aAn ideal gas is confined to a container at a temperature of 360 K. 1) What is the average kinetic energy of an atom of the gas? (Express your answer to two significant figures.) J
- I just need help with part D Problem 6: There are lots of examples of ideal gases in the universe, and they exist in many different conditions. In this problem we will examine what the temperature of these various phenomena are. Part (a) Give an expression for the temperature of an ideal gas in terms of pressure P, particle density per unit volume ρ, and fundamental constants. Answer: T = P/( ρ kB ) Part (b) Near the surface of Venus, its atmosphere has a pressure fv= 96 times the pressure of Earth's atmosphere, and a particle density of around ρv = 0.92 × 1027 m-3. What is the temperature of Venus' atmosphere (in C) near the surface? Answer: Tv = 490.55 Part (c) The Orion nebula is one of the brightest diffuse nebulae in the sky (look for it in the winter, just below the three bright stars in Orion's belt). It is a very complicated mess of gas, dust, young star systems, and brown dwarfs, but let's estimate its temperature if we assume it is a uniform ideal gas. Assume it is a…Suppose you have an ideal gas so that pV=NkT. Use the Maxwell Relations to find a solution to the partial derivative: (∂μ/∂p)T,N. Match the partial derivative to the correct solution below. a. kT/p b. p c. p/nK d. kT e. Nk/p f. p/kT g. NkTQ2/ for a monoatomic ideal gas, the partition function is: Z = e-N %3D h2B calculate F, S, P and U.
- Given the ideal gas law P V = k T, where k> 0 is a constant. We have the equation for V in terms of P and T. Finding the rate of change of the volume with respect to temperature at constant pressure, the interpretation of the result is: 1 Because this partial derivative is negative, the volume decreases as the temperature decreases at a fixed pressure. . 2. Because this partial derivative is negative, the volume increases as the temperature increases at a fixed pressure. 3. Because this partial derivative is positive, the volume increases as the temperature decreases at a fixed pressure. 4. Because this partial derivative is positive, the volume increases as the temperature increases at a fixed pressure.Figure I shows the P-V graph for a sample of a gas at 298 K. If this sample were heated to 312 K, this would be represented by a point 25. atm Figure 1 100 V/e 50 A At the top, left end of the line Off the line, above and to the right of it. B At the lower, right end of the line D Off the line, below and to the right of it.(b) Consider the following heat system on the real line: U - U = 0, XER, 1>0 %3D u(x, 0) = | sin x), rER. i. Use the fundamental solution of the heat equation to write down a solution u to the system above as an integral. ii. Show that the solution u that you have found is bounded by 1.
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