Thermodynamics, Statistical Thermodynamics, & Kinetics
3rd Edition
ISBN: 9780321766182
Author: Thomas Engel, Philip Reid
Publisher: Prentice Hall
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
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.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
(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.
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.
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Similar questions
- 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_forwardSince 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,zarrow_forwardInvestigate the dependence of pV on V for real gases.arrow_forward
- For an ideal gas obeying the ideal gas law, P = nRT/V , where R is the gas constant. Write the total differential dz and evaluate the partial derivativesarrow_forwardUse the virial equation of state to calculate the pressure exerted by 1.00 mol CH4, at 273 K confined to a volume of 1.00 cm3 , given the value of the second virial coefficient, B = -53.6 cm3 mol-1, at this temperature. You may assume that the expansion may be truncated after the second term.arrow_forwardWhat is Isothermal Expansion of a van der Waals Gas?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_forwardCalculate V−1(∂V/∂T)p,n for an ideal gas?arrow_forwardShow that CP = VT α (∂P/∂T) Sarrow_forward
- 1C.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_forwardA 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_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,
Physical Chemistry
Chemistry
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Wadsworth Cengage Learning,