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 3P
Consider a function z(x, y) and its partial derivative (∂z/∂y)x. Under what conditions is this partial derivative equal to the total derivative dz/dy?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
It is required to treat 130 kmol/hr of chloroform-air feed gas mixture that contains
12% chloroform. It is required to remove 93% of chloroform using 150 kmol/hr of
solvent that contains 99.6% water and 0.4% chloroform. The cross sectional area of the
column is 0.8 m². Calculate the column height using the following data; kx'.a = 1.35
(kmol/m³.s (Ax)), and ky'.a = 0.06 (kmol/m³.s (Ay)), kx/ky = 1.35, and the equilibrium
data are:
X 0 0.0133 0.033
y 0 0.01 0.0266
0.049 0.064 0.0747 0.0933 0.1053
0.0433 0.06 0.0733
0.111
0.1
0.12
0.14
४
B:
Find the numerical solution for the 2D equation below and calculate the temperature values for
each grid point shown in Fig. 2 (show all steps).
(Do only one trail using following initial values and show the final matrix)
[T1]
T₂
T3
[T] 1
=
[0]
0
0
d
dx
dx)
(ka)+4(ka)
=
dy
-20xy, k = 1 + 0.3 T
ge
L=3cm, 4x= Ay
B.Cs.:
at x=0=LT=0°C
at y=0-L T=10°C
Fig. (2)
: +0
العنوان
use only
Two rods fins) having same dimensions, one made orass (k = 85 Wm
K) and the mer of copper (k = 375 W/m K), having of their ends inserted
into a furna. At a section 10.5 cm a way from furnace, the temperature of
brass rod 120 Find the distance at which the ame temperature would be
reached in the per rod ? both ends are ex osed to the same environment.
ns
2.05
۲/۱
ostrar
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
- For the beam show below, draw A.F.D, S.F.D, B.M.D 6 kN/m 1 M B. 3 M Marrow_forward1. Two long rods of the same diameter-one made of brass (k=85w/m.k) and the other made of copper (k=375 w/m.k) have one of their ends inserted into a furnace (as shown in the following figure). Both rods are exposed to the same environment. At a distance of 105 mm from the furnace, the temperature of the brass rod is 120°C. At what distance from the furnace will the same temperature be reached in the copper rod? Furnace 105 mm T₁ Brass rod ⑪ h Too- x2- Ti Copper rodarrow_forward: +0 العنوان use only Two rods fins) having same dimensions, one made orass (k = 85 Wm K) and the mer of copper (k = 375 W/m K), having of their ends inserted into a furna. At a section 10.5 cm a way from furnace, the temperature of brass rod 120 Find the distance at which the ame temperature would be reached in the per rod ? both ends are ex osed to the same environment. ns 2.05 ۲/۱ ostrararrow_forward
- مشر on ۲/۱ Two rods (fins) having same dimensions, one made of brass(k=85 m K) and the other of copper (k = 375 W/m K), having one of their ends inserted into a furnace. At a section 10.5 cm a way from the furnace, the temperature brass rod 120°C. Find the distance at which the same temperature would be reached in the copper rod ? both ends are exposed to the same environment. 22.05 ofthearrow_forwardThe composite wall of oven with A= 1m² as in Fig.1 consists of three materials, two of with kA = 20 W/m K and kc = 50 W/m K with thickness, LA=0.3 m, L= 0.15 m and Lc 0.15 m. The inner surface temperature T1=900 K and the outer surface temperature T4 300 K, and an oven air temperature of To=1100 K, h=25 W/m². K. Determine kɛ and the temperatures T2 and T3 also draw the thermal resistance networkarrow_forwardTwo rods (fins) having same dimensions, one made of brass (k = 85 Wm K) and the other of copper (k = 375 W/m K), having one of their ends inserted into a furnace. At a section 10.5 cm a way from the furnace, the temperature of brass rod 120°C. Find the distance at which the same temperature would be reached in the copper rod ? both ends are exposed to the same environment. Ans 22.05arrow_forward
- A long wire (k-8 W/m °C.) with ro 5 mm and surface temperature Ts=180°C as shown in Fig.2. Heat is generated in the wire uniformly at a rate of 5 x107 W/m³. If the energy equation is given by: d 11(77) + - =0 k r dr dr Derive an expression for T(r) and determine the temperature at the center of the wire and at r=2 mm. Air Th T KA LA T2 T3 T Fig.1 KB kc 180°C Го Fig.2arrow_forwardB: Find the numerical solution for the 2D equation below and calculate the temperature values for each grid point shown in Fig. 2 (show all steps). (Do only one trail using following initial values and show the final matrix) T₂ 0 T3 0 I need a real solution, not artificial intelligence locarrow_forwardCan I solve this problem by calculating the initial kinetic energy with respect to G instead of A.arrow_forward
- B: Find the numerical solution for the 2D equation below and calculate the temperature values for each grid point shown in Fig. 2 (show all steps). (Do only one trail using following initial values and show the final matrix) T₂ 0 T3 0 locarrow_forwardShow all work. Indicate the origin that is used for each plane. Identify the Miller indices for the following planes. N 23 1 A) X B) yarrow_forwardthe following table gives weight gain time data for the oxidation of some metal at an elevated temperature W(mg/cm2). Time (min) 4.66 20 11.7 50 41.1 175 a) determin whether the oxidation kinetics obey a linear, parabolic, or logarithmic rate expression. b) Now compute W after a time of 1000 minarrow_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
What is entropy? - Jeff Phillips; Author: TED-Ed;https://www.youtube.com/watch?v=YM-uykVfq_E;License: Standard youtube license