Concept explainers
(a)
Sketch the force diagram showing that the force exerted due to the pressure of gas on either side of the element.
(a)
Answer to Problem 72CP
The force diagram is given below.
Explanation of Solution
The figure 1 below is the force diagram, which shows that the force exerted on the left and right surface due to the pressure of the gas on either side of the element.
(b)
Show that
(b)
Answer to Problem 72CP
Through calculation it is obtained that
Explanation of Solution
Consider
The net force acting on the element is the difference of the force acting on the either sides due to the pressure of the gas.
The force acting on the surface is.
Here,
Write the expression for mass in terms of volume and density.
Substitute,
Conclusion:
Equate equation (IV) and (I).
Therefore,
(c)
Derive
(c)
Answer to Problem 72CP
It is derived that
Explanation of Solution
Consider equation (V).
Substitute,
Conclusion:
Therefore, it is derived that
(d)
Prove that
(d)
Answer to Problem 72CP
The function
Explanation of Solution
Consider the given function.
Differentiate equation (VIII) with respect to
Differentiate equation (IX) with respect to
Differentiate equation (VIII) with respect to
Differentiate equation (XI) with respect to
Substitute, equation (X) and (XII) in equation (VII).
Equation (XIII) shows that the function
Conclusion:
Therefore, unction
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Chapter 17 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
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