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Show that CP = VT α (∂P/∂T) S
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- 2.00-mol of a monatomic ideal gas goes from State A to State D via the path A→B→C→D: State A PA=13.0atm, VA=11.50L State B PB=13.0atm, VB=6.00L State C PC=21.5atm, VC=6.00L State D PD=21.5atm, VD=21.50L Assume that the external pressure is constant during each step and equals the final pressure of the gas for that step. Calculate q for this process. Calculate w for this process. Calculate ΔE for this process Calculate ΔH for this process.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,zCalculate V−1(∂V/∂T)p,n for an ideal gas?
- P2D.2 Starting from the expression Cp − CV = T(∂p/∂T)V(∂V/∂T)p, use theappropriate relations between partial derivatives (The chemist’s toolkit 9 inTopic 2A) to show thatC CT V TV p( / )( / ) p VpT2− = ∂ ∂∂ ∂ Use this expression to evaluate Cp − CV for a perfect gas.A 0.250 mol nitrogen initially at 50 °C with a volume of 8.00 L is allowed to expand reversibly and adiabatically until its volume has doubled. Calculate the value of ΔHwhen Cp = 7/2R.Rank the elements or compounds in the table below in decreasing order of their boiling points. That is, choose 1 next to the substance with the highest boiling point, choose 2 next to the substance with the next highest boiling point, and so on. substance A B с D H :0: H | || | H с C -C-H 174 H H H chemical symbol, chemical formula or Lewis structure H H H | | C I 1 I H H H (II | Ag - Ar - :O: -O-H boiling point (Choose one) (Choose one) ✓ (Choose one) (Choose one) ✓
- Two nitro (NO,) groups are chemically bonded to a patch of surface. They can't move to another location on the surface, but they can rotate (see sketch at right). It turns out that the amount of rotational kinetic energy each NO, group can have is required to be a multiple of ɛ, 2 where ɛ = 1.0 × 10 -24 J. In other words, each NO, group could have ɛ of rotational kinetic energy, or 2ɛ, or 3ɛ, and so forth – but it cannot have just any old amount of rotational kinetic energy. Two rotating NO, groups Suppose the total rotational kinetic energy in this system is initially known to be 87ɛ. Then, some heat is removed bonded to a surface. from the system, and the total rotational kinetic energy falls to 66ɛ. Calculate the change in entropy. Round your answer to 3 significant digits, and be sure it has the correct unit symbol. 믐 ?Indicate whether each statement is true or false. (a) Unlikeenthalpy, where we can only ever know changes in H, wecan know absolute values of S. (b) If you heat a gas suchas CO2, you will increase its degrees of translational, rotationaland vibrational motions. (c) CO2(g) and Ar(g) havenearly the same molar mass. At a given temperature, theywill have the same number of microstates.Two nitro (NO,) groups are chemically bonded to a patch of surface. They can't move to another location on the surface, but they can rotate (see sketch at right). It turns out that the amount of rotational kinetic energy each NO, group can have is required to be a multiple of ɛ, where 8= 1.0 x 10 -24 J. In other words, each NO, group could have ɛ of rotational kinetic energy, or 2ɛ, or 3ɛ, and so forth - but it cannot have just any old amount of rotational kinetic energy. Two rotating N0, groups Suppose the total rotational kinetic energy in this system is initially known to be 41ɛ. Then, some heat is removed from the bonded to a surface. system, and the total rotational kinetic energy falls to 30ɛ. Calculate the change in entropy. Round your answer to 3 significant digits, and be sure it has the correct unit symbol. Check 2021 McGraw-Hill Education All Rights Reserved Tems of Uhe Privacy Accesbil Explanation MacBook Air olo
- Rearrange the van der Waals equation of state, p = nRT/(V − nb) − n2a/V2(Topic 1C) to give an expression for T as a function of p and V (with n constant). Calculate (∂T/∂p)V and confirm that (∂T/∂p)V = 1/(∂p/∂T)V.(a) Express (∂Cp/∂P)T as a second derivative of H and find its relation to (∂H/∂P)T. (b) From the relationships found in (a), show that (∂Cp/∂V)T=0 for a perfect gas.At 1 atm, how much energy is required to heat 95.0 g H2O(s)] at −14.0 ∘C to H2O(g) at 115.0 ∘C? Use the heat transfer constants.