Thermodynamics: An Engineering Approach
9th Edition
ISBN: 9781259822674
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 12.6, Problem 104FEP
For a gas whose equation of state is P(v − b) = RT, the specified heat difference cp − cv is equal to
- (a) R
- (b) R − b
- (c) R + b
- (d) 0
- (e) R(1 + v/b)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
p/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+1
(b)
A fixed mass of the ideal gas argon initially occupies a volume of 3 litres at a
pressure of 3 MPa. An isometric process, followed by an isentropic process, brings
the gas to an equilibrium state at 400°C, 4 MPa and 4 litres volume. An isobaric
process finally brings the gas back to a different equilibrium state at the initial
temperature. Determine:
(i)
the mass of gas in the closed system.
(ii)
the temperature, volume, and pressure of the gas, at each of the four
states.
(iii) the overall change in entropy between the initial and final states.
(iv) the work transfer in each of the three processes and the overall work
transfer.
(Argon: CP= 520.3 Jkg ¹K-¹, R= 208.1 Jkg-¹K-¹)
The van der Wails equation of state is p ± (v-b = RT,
where p is pressure, v is specific volume, T is
temperature and R is characteristic gas constant The SI
unit of a is
Chapter 12 Solutions
Thermodynamics: An Engineering Approach
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
- In general, when a system undergoes a change from state 1 to state 2, the change in enthalpy is given by: deltaH = deltaU + PdeltaV + VdeltaP + deltaPdeltaV Derive this equation from the First Law of Thermodynamics, indicating the conditions assumed for the derivation.arrow_forwardQ3: In a closed vessel with a volume of 50 dm3 there are 2 moles of an ideal monoatomic gas with cv, m = 12.471 J K-1 mol-1 at 25°C. The vessel was heated to 125°C. Calculate the values of Q, W, AU, AH in Joules and the initial and final pressure in the system. R = 8,314 J K-1 mol-1. Cp,m = 20,785 J K-1 mol-1arrow_forwardOne kilogram of water (V1 = 1003 cm3.kg−1) in a piston/cylinder device at 25°C and 1 bar is compressed in a mechanically reversible, isothermal process to 1500 bar. Determine Q, W, ΔU, ΔH, and ΔS given that β = 250 × 10−6 K−1 and κ = 45 × 10−6 bar−1. A satisfactory assumption is that V is constant at its arithmetic average value.arrow_forward
- If 1 mole of ideal monoatomic gas experiments a reversible process in two stages, first isobar and then isotherm, which goes from 1atm and 20 ° C to 0.5 atm and 40 ° C. Determine the energy exchanged in the form of heat. Ans: AE = -609 cal/mol; W = 609 cal/mol; Q = 531.9 cal.arrow_forwardKrypton in a closed system is compressed adiabatically from 74 K and 1 bar to a final pressure of 24 bar. What is the final temperature in K? Assume krypton is an ideal gas. From Appendix B in the text, we can assume the heat capacity of krypton is independent of temperature and CP=2.5R , where R is the molar gas constant R=8.314 J/(mol K). For an ideal gas, recall CV=CP−R=1.5R. Report your answer in units of K using three decimal places.arrow_forwardEntropy is one of the important coordinates in thermodynamics. Entropy shows the ratio of heat absorbed or rejected by temperature so that it can indicate the direction of heat flow. Entropy is useful for knowing the internal energy efficiency. Derive an equation for the change in the internal energy of a gas that satisfies the van der Waals equation of state. Assume the value of Cv satisfies the relationship: Cv=c1 + c2T, with c1 and c2 constant *application of the 3rd law of thermodynamicsarrow_forward
- A gas undergoes isobaric expansion at 0.05 bar from 0.1 m³ to 1.0 m³ when 2.0 KiloJoules of heat is applied to it. Which of the following is true regarding the work, heat and the change in internal energy involed in this change (all quantities in KiloJoules)? A. +4.5, -2.0, +2.5 B. -4.5, +2.0, -2.5 C. +4.5, +2.0, +6.5 D. -4.5, -2.0, -6.5arrow_forwardFrom Boyle and Charles's law, prove that the ideal gas equation looks like this:arrow_forwardQ3/ A 5.0-m tank is charged with 75.0 kg of propane gas at 25°C. Use the SRK equation of state to estimate the pressure in the tank; then calculate the percentage error that would result from the use of the ideal gas equation of state for the calculation. C;Hg: Te = 369.9 K Pc = 42.0 atm(4.26 x 10° Pa) @= 0.152 %3D (RT.)? a = 0.42747 Pc RTc = 0.08664 Pc b m = 0.48508 + 1.55171w – 0.1561o- T; = T/Te %3D a = |1 + m RT P = aa V(Û + b)arrow_forward
- Entropy is one of the important coordinates in thermodynamics. Entropy shows the ratio of heat absorbed or rejected by temperature so that it can indicate the direction of heat flow. Entropy is useful for knowing the internal energy efficiency. Derive an equation for the change in the internal energy of a gas that satisfies the van der Waals equation of state. Assume the value of Cv satisfies the relationship: Cv=c1 + c2T, with c1 and c2 constantarrow_forwardDefine the van der Waals Equation of State.arrow_forwardKnowing that a system follows the equation of state S5 U = k- V 2 where k is a constant. Find the expressions for the equation of state in terms of P, V and T and a relation between of any two of these thermodynamic functions valid for an adiabatic process.arrow_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
Thermodynamics - Chapter 3 - Pure substances; Author: Engineering Deciphered;https://www.youtube.com/watch?v=bTMQtj13yu8;License: Standard YouTube License, CC-BY