Drow and explainthe use of vr data for calculating the final temperature during an isentropic process

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter8: Natural Convection
Section: Chapter Questions
Problem 8.3P
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Drow and explainthe use of vr data for calculating the final temperature during an isentropic process

Expert Solution
Step 1

The use of Vr data for calculating the final temperature during an isentropic process can be easily explained by taking an example.

Now let us take an example of Isentropic compression of Air in a car engine.

 

In this example consider air is compressed in a car engine from T1 K and P1 KPa in a reversible and adiabatic manner. If the compression ratio of this engine is V1/V2, determine the final temperature (T2)

Here in the above example, the process is easily recognized as being isentropic since it is both reversible and adiabatic.

Step 2

Now with the help of relative specific volume data (Vr) from the relative specific volume table, we can calculate the final temperature as:

Mechanical Engineering homework question answer, step 2, image 1

Where a and b are the constants determined from boundary conditions, Vr1 is the relative specific volume at point 1 and Vr2 is the relative specific volume at point 2.

Now corresponding to temperature T1 we can find the value of Vr1 from a relative specific volume table and then putting the values in the above equation for finding Vr2.

Now corresponding to Vr2 from a relative specific volume table we can determine the final temperature T2.

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