Concept explainers
What is the difference between partial differentials and ordinary differentials?
The difference between partial differentials and ordinary differentials.
Explanation of Solution
In ordinary differentials, the total derivative of the function is depends on a single variable alone.
For example:
Consider the function
The total derivative of function
In partial differentials, the total derivative of the function is depends on two variables.
For example:
Consider the function
The total derivative of function
Here, the function
Want to see more full solutions like this?
Chapter 12 Solutions
Thermodynamics: An Engineering Approach ( 9th International Edition ) ISBN:9781260092684
- A heating element made of tungsten wire connected to a large battery that has negligible internal resistance. When the heating element reaches 80.0°C, it consumes electrical energy at a rate of 480 W. Assume that the temperature coefficient of resistivity has the value given in Table 25.2 in the textbook and that it is constant over the temperature range in this problem. In the equation R(T) = Ro [1 + a(T - To)] take To to be 20.0°C. Part A What is its power consumption when the temperature of the heating element is 110.0°C? Express your answer with the appropriate units. P = Submit Value Provide Feedback Request Answer Units ?arrow_forwardEvaluate the thermal efficiency for each case (A, B, C and D) and obtain the optimal case which represent the highest thermal efficiency case. Explain your choice using a T-S diagramarrow_forwardIDerive the value of thermal resistance in aCylindrical wallarrow_forward
- The subject is Mechanics of Deformable Bodies. Please answer problem 1 to 5. Please Im begging you. PLEASE thank youarrow_forwardDerive the relation between the coefficient of linear thermal expansion and coefficient of area (volume) thermal expansion?arrow_forwardThe cross-sectional area of a conical piece made of pure aluminum has a diameter D = a.x ^ 1/2 and a = 0.5m ^ 1/2.The left edge surface of the part is at x1 = 25 mm, and the right edge surface is x2 = 125 mm. Edge temperatures are T1 = 600K and T2 = 400K and the side surface is completely insulated.a) Assuming that the heat conduction is one dimensional, write a relation for the temperature distribution T (x).b) Calculate the heat transfer.arrow_forward
- Name the processes by which heat can be transferred from one place to another. Which one does not require a medium?arrow_forwardQ#01: Write a short note on What are the best possible solutions to increase the heat transfer rate of a body.Which material will transfer more heat? Either a material with thermal conductivity ? = 121 or ? = 22 . Justify your answer. Explain the Fouling phenomenon. What is the effect of fouling on heat transfer rate?arrow_forwardThermal Conductivity of Skin" Design experiments and calculate heat transfer coefficients/thermal conductivity (k)arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY