THERMODYNAMICS (LL)-W/ACCESS >CUSTOM<
9th Edition
ISBN: 9781266657610
Author: CENGEL
Publisher: MCG CUSTOM
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 12.6, Problem 43P
Derive an expression for the specific heat difference cp − cv for (a) an ideal gas, (b) a van der Waals gas, and (c) an incompressible substance.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
0.25kg/s of Catbon Dioxide (R 0.1889 kJ/kg-K, k 1.289) undergo a certain process in a close
system from initial volume and temperature of 268cm' and 134K to a final volume and temperature
of 804cm' and 402K respectively. From the data given, perform necessary analysis in determining
the type of process to further solve the following questions as follow:
a. Work done by/on the system (kJ/s)
b. Change in Entropy (kW/K)
c. Heat added/rejected by the system (kJ/s)
The initial state of 1.00 mol of a dilute gas is P1 = 3.00 atm, V1 = 1.00 L, and Eint 1 = 456 J and
its final state is P2 = 2.00 atm, V2 = 3.00 L, and Eint2 = 912 J. The gas is first cooled at constant
volume until it reaches its final pressure. It is then allowed to expand at constant pressure until it
reaches its final volume. (a) Illustrate this process on a PV diagram and calculate the work done by
the gas. (b) Find the heat absorbed by the gas during this process.
An ideal gas is adiabatically expanded along path AB from a temperature
T=500 K to 300 K, and then isochorically heated along a path BC back to
T=500 K.
(i) Draw a pressure-volume diagram for this process and show that the ratio of
pressures at points A and C obeys
(3)
PA
PC
where y is the adiabatic index of the ideal gas.
(ii) Given that the ratio of pressures at points A and C is found to be
PA
3.59
PC
Chapter 12 Solutions
THERMODYNAMICS (LL)-W/ACCESS >CUSTOM<
Ch. 12.6 - What is the difference between partial...Ch. 12.6 - Consider the function z(x, y). Plot a differential...Ch. 12.6 - Consider a function z(x, y) and its partial...Ch. 12.6 - Prob. 4PCh. 12.6 - Prob. 5PCh. 12.6 - Consider a function f(x) and its derivative df/dx....Ch. 12.6 - Conside the function z(x, y), its partial...Ch. 12.6 - Consider air at 350 K and 0.75 m3/kg. Using Eq....Ch. 12.6 - Consider air at 350 K and 0.75 m3/kg. Using Eq....Ch. 12.6 - Nitrogen gas at 800 R and 50 psia behaves as an...
Ch. 12.6 - Consider an ideal gas at 400 K and 100 kPa. As a...Ch. 12.6 - Using the equation of state P(v a) = RT, verify...Ch. 12.6 - Prove for an ideal gas that (a) the P = constant...Ch. 12.6 - Verify the validity of the last Maxwell relation...Ch. 12.6 - Verify the validity of the last Maxwell relation...Ch. 12.6 - Show how you would evaluate T, v, u, a, and g from...Ch. 12.6 - Prob. 18PCh. 12.6 - Prob. 19PCh. 12.6 - Prob. 20PCh. 12.6 - Prove that (PT)=kk1(PT)v.Ch. 12.6 - Prob. 22PCh. 12.6 - Prob. 23PCh. 12.6 - Using the Clapeyron equation, estimate the...Ch. 12.6 - Prob. 26PCh. 12.6 - Determine the hfg of refrigerant-134a at 10F on...Ch. 12.6 - Prob. 28PCh. 12.6 - Prob. 29PCh. 12.6 - Two grams of a saturated liquid are converted to a...Ch. 12.6 - Prob. 31PCh. 12.6 - Prob. 32PCh. 12.6 - Prob. 33PCh. 12.6 - Prob. 34PCh. 12.6 - Prob. 35PCh. 12.6 - Prob. 36PCh. 12.6 - Determine the change in the internal energy of...Ch. 12.6 - Prob. 38PCh. 12.6 - Determine the change in the entropy of helium, in...Ch. 12.6 - Prob. 40PCh. 12.6 - Estimate the specific heat difference cp cv for...Ch. 12.6 - Derive expressions for (a) u, (b) h, and (c) s for...Ch. 12.6 - Derive an expression for the specific heat...Ch. 12.6 - Derive an expression for the specific heat...Ch. 12.6 - Derive an expression for the isothermal...Ch. 12.6 - Prob. 46PCh. 12.6 - Show that cpcv=T(PT)V(VT)P.Ch. 12.6 - Show that the enthalpy of an ideal gas is a...Ch. 12.6 - Prob. 49PCh. 12.6 - Show that = ( P/ T)v.Ch. 12.6 - Prob. 51PCh. 12.6 - Prob. 52PCh. 12.6 - Prob. 53PCh. 12.6 - Prob. 54PCh. 12.6 - Prob. 55PCh. 12.6 - Does the Joule-Thomson coefficient of a substance...Ch. 12.6 - The pressure of a fluid always decreases during an...Ch. 12.6 - Will the temperature of helium change if it is...Ch. 12.6 - Estimate the Joule-Thomson coefficient of...Ch. 12.6 - Estimate the Joule-Thomson coefficient of...Ch. 12.6 - Prob. 61PCh. 12.6 - Steam is throttled slightly from 1 MPa and 300C....Ch. 12.6 - What is the most general equation of state for...Ch. 12.6 - Prob. 64PCh. 12.6 - Consider a gas whose equation of state is P(v a)...Ch. 12.6 - Prob. 66PCh. 12.6 - What is the enthalpy departure?Ch. 12.6 - On the generalized enthalpy departure chart, the...Ch. 12.6 - Why is the generalized enthalpy departure chart...Ch. 12.6 - What is the error involved in the (a) enthalpy and...Ch. 12.6 - Prob. 71PCh. 12.6 - Saturated water vapor at 300C is expanded while...Ch. 12.6 - Determine the enthalpy change and the entropy...Ch. 12.6 - Prob. 74PCh. 12.6 - Prob. 75PCh. 12.6 - Prob. 77PCh. 12.6 - Propane is compressed isothermally by a...Ch. 12.6 - Prob. 81PCh. 12.6 - Prob. 82RPCh. 12.6 - Starting with the relation dh = T ds + vdP, show...Ch. 12.6 - Using the cyclic relation and the first Maxwell...Ch. 12.6 - For ideal gases, the development of the...Ch. 12.6 - Show that cv=T(vT)s(PT)vandcp=T(PT)s(vT)PCh. 12.6 - Temperature and pressure may be defined as...Ch. 12.6 - For a homogeneous (single-phase) simple pure...Ch. 12.6 - For a homogeneous (single-phase) simple pure...Ch. 12.6 - Prob. 90RPCh. 12.6 - Prob. 91RPCh. 12.6 - Estimate the cpof nitrogen at 300 kPa and 400 K,...Ch. 12.6 - Prob. 93RPCh. 12.6 - Prob. 94RPCh. 12.6 - Prob. 95RPCh. 12.6 - Methane is to be adiabatically and reversibly...Ch. 12.6 - Prob. 97RPCh. 12.6 - Prob. 98RPCh. 12.6 - Prob. 99RPCh. 12.6 - An adiabatic 0.2-m3 storage tank that is initially...Ch. 12.6 - Prob. 102FEPCh. 12.6 - Consider the liquidvapor saturation curve of a...Ch. 12.6 - For a gas whose equation of state is P(v b) = RT,...Ch. 12.6 - Prob. 105FEPCh. 12.6 - Prob. 106FEP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Derive a relation for the volume expansivity β and the isothermal compressibility κ (a) for an ideal gas and (b) for a gas whose equation of state is P(v - a) = RT and (c) calculate β and κ for nitrogen at T=175K, v = 0.00375 m3 /kg, and a = 0.00138 m3 /kg and compare the results obtained from ideal gas law and from P(v - a) = RT.arrow_forwardThe volume and temperature of air (assumned to be an ideal gas) in a closed vessel is 2.87 m3 and 300 K, respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is 0.5 bar. If the gas constant of air is R= 287 J/kgK %3D and the atmospheric pressure is 1 bar, the mass of air (in kg) in the vessel isarrow_forwardp/atm 2.0 1.0 EXERCISE 3 (c) 3 1 thermal (b) Ⓡ One mole of an ideal gas undergoes a cyclic three-step process according to Figure 2: (a) 1->2: reversible and adiabatic expansion starting at T₁, and pressure = 2 atm. pl (b) 2->3: reversible isothermal compression up to p3 = 1 atm and (c) 3->1: heating under constant volume, at final temperature Ti, and pressure p1 = 2 atm. Calculate the entropy changes of the gas for the three steps and for the cycle. The heat capacity under constant volume is given: cx= 12.47 J mol-¹ K-¹. V Enter your results (with units) in the Table below AS₁1+2 AS2+3 AS3+1 AS1+2+3+1arrow_forward
- Derive an expression for the specific heat difference of a substance whose equation of state is: P=[(RT)/(v-b)]-[a/(v*(v+b)*T1/2)] Where a and b are empirical constantsarrow_forwardA 0.5 m3 tank contains methane CH4 at 20.68 bar and 38 degrees celsius. Using Avogadro's principle, find the mass of carbon dioxide CO2 (in kg) subjected to the same pressure and temperature in a 3.8-m3 tankarrow_forward1 kg of gas occupying 0.19 m' at a pressure of 15 bar is heated at constant pressure until its volume is 0.35 m'. The gas is then expanded adiabatically until its volume is 2 m'. Calculate: 1- Temperature at the end of constant pressure heating and the end of adiabatic expansion. Take Cp = 1.068 kJ/kg.K and Cv=0.775 kJ/kg.K. 2- Total work done.arrow_forward
- Who is right? A student thinks that in the open air at 25°C, water vaporizes slowly, and therefore finds in the presence of its steam. Or a student referring to the water state diagram and under an atmosphere water claims that water can only be entirely in liquid form. To which Error of reasoning is due to this "contradiction"?arrow_forwardplot the polytropic process on P- V and T- S diagrams: Air endothermic, volume decrease, heating, and pressure increase, and point out the range of polytropic index.arrow_forwardNiloarrow_forward
- 2. For a certain gas, R = 0.377KJ/kg.K and k = 1.384. (a)What are the values of c, and a, ? (b) What mass of this gas would occupy a volume of 0.552 m at 517.11 kPa and 36.7 deg. Celsius? (c) If 31.65 kJ is transferred to this gas at constant volume, what are the resulting temperature and pressure? Use 2kgmarrow_forwardPLEASE HELP ANSWER THIS THERMODYNAMICS PRACTICE QUESTIONarrow_forwardConsider water (H2O) at 320C and 6 Mpa. Determine the error in the specific volume predicted by the ideal gas law relative to the actual value. The molar mass of H2O is 18.02 g/molarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
First Law of Thermodynamics, Basic Introduction - Internal Energy, Heat and Work - Chemistry; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=NyOYW07-L5g;License: Standard youtube license