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- (*), (*): P Use the Euler and reciprocal relations to show that it is equivalent to Cp - Cy = T Ср - Cv = −T. Сү = -Т. Әр ат av 2 T (1) (2) Use this expression to evaluate Cр - Cv for (1) an ideal gas, and (2) for a van der Waals gas.Deduce the relation pv = nRT where R is a constant called universal.Q9 + Show that, for a perfect gas, (US)y= T and (@U/V)₁=-p.
- Since we will be dealing with partial derivatives later in the semester, this is a good opportunity to review this topic (see appendix C). Then evaluate the following partial derivatives (a) PV = nRT; (∂ P/∂V)T (b) r = (x2 + y2 + z 2 )1/2; (∂ r/∂y)x,zGiven these relation, prove this without usin Maxwell relatios as - ( ), aV ӘT JP/T P5. At its normal boiling point (337.3 K), methanol (CH3OH) has AvapH = 25.79 kJ/mol, and the densities of its liquid and vapor states at that temperature are 0.7486 g/mL and 0.0.001206 g/mL, respectively. %3D Data from dT (a) Use the Clapeyron equation to determine the value of () for methanol at T = 337.3 K. dP. Report your answer in units of K/bar. (b) Use your result to estimate its boiling point (in K) at a pressure of 2 bars. 3.
- (ii) Given that ан (он), =C, au - (24) = C₁ Show that Cp - Cy =nRT for n moles of an ideal gas and that112. Main assumption(s) involved in the derivation of Debye-Hückel equation is(are) the validity of (a) Only Poission equation (b) Poission equation and Boltzmann distribution (c) Poission equation, Boltzmann distribution and |±Zep|>>kÂT (d) Poission equation Boltzmann distribution and |±Zep|<Calculate the kinetic energy of Ne, Ar. and Kr at 287 K. Enter your answers numerically separated by commas. VE KNe, Kar, KKr = 3.58 Submit ΑΣΦ C - 21 ● 10 2¹,3.57 10 2¹,3.57 • 10-2¹,3.57 • 10-21 Previous Answers Request Answer ? J/mol1C.5 The virial equation of state may also be written as an expansion in terms of pressure: Z= 1 + B'p+ ... The critical constants for water, H,0, are 218.3 atm, 55.3 cm³ mol-1 and 647.4 K. Assuming that the expansion may be truncated after the second term, calculate the value of the second virial coef- ficient B'at the critical temperature. %3DUsing the following data O2 (g) SO₂ (g) SO3 (g) Af He/kJ mol-1 0 -296.8 -395.7 AfGe/kJ mol-1 0 -300.2 -371.1 5/JK-1 mol-1 205.1 248.2 256.8 ACO/JK-¹ mol-1 29.4 39.9 50.7 In the following reaction SO₂(g) + O₂(g) → SO3(g) Calculate the enthalpy of reaction, the entropy of reaction, and the Gibbs free energy of the reaction at P=1 atm and T-800 K.3. At T = 300K, 1bar of ¹60¹80 in a 1m³ box (lengths ax ay = az = 1m) can be considered as an ideal gas. In that case, the average translational energy in each dimension for a molecule is given by: Ex = Ex = Ex = 1kT, where k = 1.38 x 10-23 J/K is the Boltzmann constant. The average rotational energy about an axis perpendicular to the O=O bond is: Erot=kT, Evib = KT. and the average vibrational energy is: Given that the fundamental vibrational frequency for ¹60¹80 is w = 4.741 x 10¹³ Hz, find the values of the quantum numbers nx, J, and u for an average ¹60¹80 molecule in this system.SEE MORE QUESTIONS