Thermodynamics, Statistical Thermodynamics, & Kinetics
3rd Edition
ISBN: 9780321766182
Author: Thomas Engel, Philip Reid
Publisher: Prentice Hall
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Chapter 3, Problem 3.35NP
Derive the equation
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The density of lead is 1.13 ✕ 104 kg/m3 at 20.0°C. Find its density (in kg/m3) at 100°C. (Use ? = 29 ✕ 10−6 (°C)−1 for the coefficient of linear expansion. Give your answer to at least four significant figures.)
(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.
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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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- A sample of 2.2 mol CO2(g) is originally confined in 15 dm3 at 280 K and then undergoes adiabatic expansion against a constant pressure of 78.5 kPa until the volume has increased by a factor of 4.0. Calculate ΔT. (The final pressure of the gas is not necessarily 78.5 kPa.)arrow_forwardCalculate V−1(∂V/∂T)p,n for an ideal gas?arrow_forwardThe cohesive energy density, U, is defined as U/V, where U is the mean potential energy of attraction within the sample and V its volume. Show that U = 1/2N2∫V(R)dτ where N is the number density of the molecules and V(R) is their attractive potential energy and where the integration ranges from d to infinity and over all angles. Go on to show that the cohesive energy density of a uniform distribution of molecules that interact by a van der Waals attraction of the form −C6/R6 is equal to −(2π/3)(NA2/d3M2)ρ2C6, where ρ is the mass density of the solid sample and M is the molar mass of the molecules.arrow_forward
- A sample of 4.50 g of methane occupies 12.7 dm³ at 310 K. (a) Calculate the work done when the gas expands isothermally against a constant external pressure of 200 Torr until its volume has increased by 3.3 dm³. (b) Calculate the work that would be done if the same expansion occurred reversibly.arrow_forwardAt low temperatures the heat capacity of Ag(s) is found to obey the Debye law Cp,m = aT 3, with a = 1.956 × 10−4 J K−4 mol−1. Determine Sm(10 K) − Sm(0) for silver.arrow_forward2.00-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.arrow_forward
- A sample of methane of mass 45.00 g initially occupies 13.11 L at 310.0 K. Calculate the work done when the gas expands isothermally and reversiblly until its volume increases to 17.41 L. 1 Torr = 133.33 Pa; MW of methane = 16.04 g/mol and R=8.3145 J/K mol. W = J. 4 sig. fig.arrow_forward(c) The work done by helium on a balloon was 1.659 kJ. If o.95 mol of helium was allow to expand to 18 L at a constant temperature of 30 °C. What was the initial volume of the gas used?arrow_forwardEstimate the values of γ = Cp,m/CV,m for gaseous ammonia and methane. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the experimental value at 25 °C? Hint: Note that Cp,m − CV,m = R for a perfect gas.arrow_forward
- The French chemists, Pierre L. Dulong and Alexis T. Petit, noted in 1819 that the molar heat capacity of many solids at ordinary temperatures is proportional to the number of atoms per formula unit of the solid. They quantified their observations in what is known as Dulong and Petit's rule, which says that the molar heat capacity, Cp, of a solid can be expressed as Cp = N. 3R where N is the number of atoms per formula unit and R is the universal gas constant. The observed heat capacity per gram of a compound containing rubidium and oxygen is 0.64 J · K¯¹ · g¯¹. Use Dulong and Petit's rule to determine the empirical formula of the compound. empirical formula: Rb5O Incorrectarrow_forwardThe French chemists, Pierre L. Dulong and Alexis T. Petit, noted in 1819 that the molar heat capacity of many solids at ordinary temperatures is proportional to the number of atoms per formula unit of the solid. They quantified their observations in what is known as Dulong and Petit's rule, which says that the molar heat capacity, Cp, of a solid can be expressed as Cp = N. 3R where N is the number of atoms per formula unit and R is the universal gas constant. -1 The observed heat capacity per gram of a compound containing rubidium and oxygen is 0.64 J · K¯¹ . g¯¹. Use Dulong and Petit's rule to determine the empirical formula of the compound. empirical formula: Rb5O Incorrectarrow_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_forward
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