Thermodynamics, Statistical Thermodynamics, & Kinetics
3rd Edition
ISBN: 9780321766182
Author: Thomas Engel, Philip Reid
Publisher: Prentice Hall
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Chapter 3, Problem 3.21NP
Interpretation Introduction
Interpretation:The expression for the total differential dP in terms of dV and dT needs to be determined for the van der Waals equation of state. This needs to be determined whether dP is an exact differential or not.
Concept Introduction:
Different thermodynamic properties like enthalpy, entropy, free energy etc. are used to define different properties like volume, pressure and heat capacity.
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(a) Write expressions for dV and dp given that V is a function of p and T and p is a function of V and T. (b) Deduce expressions for d ln V and d ln p in terms of the expansion coefficient and the isothermal compressibility.
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,z
(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.
Chapter 3 Solutions
Thermodynamics, Statistical Thermodynamics, & Kinetics
Ch. 3 - Prob. 3.1CPCh. 3 - Prob. 3.2CPCh. 3 - Prob. 3.3CPCh. 3 - Prob. 3.4CPCh. 3 - Why can qv be equated with a state function if q...Ch. 3 - Prob. 3.6CPCh. 3 - Prob. 3.7CPCh. 3 - Prob. 3.8CPCh. 3 - Prob. 3.9CPCh. 3 - Why is qv=U only for a constant volume process? Is...
Ch. 3 - Prob. 3.11CPCh. 3 - Why are q and w not state functions?Ch. 3 - Prob. 3.13CPCh. 3 - What is the relationship between a state function...Ch. 3 - Prob. 3.15CPCh. 3 - Is the following statement always, never, or...Ch. 3 - Is the following statement always, never, or...Ch. 3 - Prob. 3.18CPCh. 3 - Prob. 3.19CPCh. 3 - Is the expression UV=T2T1CVdT=nT1T2CV,mdT only...Ch. 3 - Prob. 3.1NPCh. 3 - Prob. 3.2NPCh. 3 - Prob. 3.3NPCh. 3 - Prob. 3.4NPCh. 3 - Prob. 3.5NPCh. 3 - Prob. 3.6NPCh. 3 - Integrate the expression =1/VV/TP assuming that ...Ch. 3 - Prob. 3.8NPCh. 3 - Prob. 3.9NPCh. 3 - Prob. 3.10NPCh. 3 - Prob. 3.11NPCh. 3 - Calculate w, q, H, and U for the process in which...Ch. 3 - Prob. 3.13NPCh. 3 - Prob. 3.14NPCh. 3 - Prob. 3.15NPCh. 3 - Prob. 3.16NPCh. 3 - Prob. 3.17NPCh. 3 - Prob. 3.18NPCh. 3 - Prob. 3.19NPCh. 3 - Prob. 3.20NPCh. 3 - Prob. 3.21NPCh. 3 - Prob. 3.22NPCh. 3 - Derive the following relation, UVmT=3a2TVmVm+b for...Ch. 3 - Prob. 3.24NPCh. 3 - Prob. 3.25NPCh. 3 - Prob. 3.26NPCh. 3 - Prob. 3.27NPCh. 3 - Prob. 3.28NPCh. 3 - Prob. 3.29NPCh. 3 - Prob. 3.30NPCh. 3 - Prob. 3.31NPCh. 3 - Prob. 3.32NPCh. 3 - Prob. 3.33NPCh. 3 - Prob. 3.34NPCh. 3 - Derive the equation H/TV=CV+V/k from basic...Ch. 3 - Prob. 3.36NPCh. 3 - Prob. 3.37NPCh. 3 - Show that CVVT=T2PT2VCh. 3 - Prob. 3.39NP
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- 2. Evaluate the following integrals. ● -5 dx 5x • S√1 + x dx 3. The pressure of one mole of a van der Waals gas is a function of volume and temperature. Determine if dP is an exact or inexact differential. P ---- RT V-b a V2arrow_forward(a) Derive, given that dU = dq+ dw, and considering that dU is an exact differential, a general relation between Cy and Cp. (b) Consequently, assume ideal gas behaviour and simplify your result.arrow_forwardWhat is Isothermal Expansion of a van der Waals Gas?arrow_forward
- Investigate the dependence of pV on V for real gases.arrow_forward(*), (*): 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.arrow_forwardShow that CP = VT α (∂P/∂T) Sarrow_forward
- Calculate V−1(∂V/∂T)p,n for an ideal gas?arrow_forward1C.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. %3Darrow_forward3. 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.arrow_forward
- 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.arrow_forwardCalculate the work done during the isothermal reversible expansion of a gas that satisfies the virial equation of state (eqn 1C.3b) written with the first three terms. Evaluate (a) the work for 1.0 mol Ar at 273 K (for data, see Table 1C.3) and (b) the same amount of a perfect gas. Let the expansion be from 500 cm3 to 1000 cm3 in each case.arrow_forwardDerive the Boyle Temperaturearrow_forward
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