(a)
The angle between the invar bars.
(a)
Answer to Problem 54AP
The angle between the invar bars is
Explanation of Solution
The diagram for the three metal bars is depicted below.
Write the equation angle from trigonometry.
Here,
Write the equation for the final length.
Here,
Conclusion:
Substitute
Thus, the angle between the invar bars is
(b)
The value of angle is accurate for both negative and positive temperature or not.
(b)
Answer to Problem 54AP
Yes, the value of angle is accurate for both negative and positive temperature.
Explanation of Solution
If the temperature difference positive or negative, it will not affect the value of angle.
If the temperature is positive, the bar will expand. As well as the temperature i negative, the bar will have contraction.
Thus, the value of angle is accurate for both negative and positive temperature.
(c)
The value of angle is accurate for zero degree temperature or not.
(c)
Answer to Problem 54AP
Yes, the value of angle is accurate for zero degree temperature.
Explanation of Solution
Write the expression for the angle.
At,
Thus, the value of angle is accurate for zero degree temperature.
(d)
The angle between the invar bars when the invar also expand.
(d)
Answer to Problem 54AP
The angle between the invar bars when the invar also expand is
Explanation of Solution
Refer Figure 1.
Write the equation angle from trigonometry.
Here,
Write the equation for the final length of the aluminium.
Here,
Write the equation for the final length of the invar.
Here,
Conclusion:
Substitute
Thus, the angle between the invar bars when the invar also expand is
(e)
The greatest value of angle between the invar bars.
(e)
Answer to Problem 54AP
The greatest value of angle between the invar bars is
Explanation of Solution
Write the equation for the angle
Conclusion:
Substitute
Thus, the greatest value of angle between the invar bars is
(f)
The smallest value of angle between the invar bars.
(f)
Answer to Problem 54AP
The smallest value of angle between the invar bars is
Explanation of Solution
Write the equation for the angle
Conclusion:
Substitute
Thus, The smallest value of angle between the invar bars is
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Chapter 19 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
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- A hollow aluminum cylinder 20.0 cm deep has an internal capacity of 2.000 L at 20.0C. It is completely filled with turpentine at 20.0C. The turpentine and the aluminum cylinder are then slowly warmed together to 80.0C. (a) How much turpentine overflows? (b) What is the volume of the turpentine remaining in the cylinder at 80.0C? (c) If the combination with this amount of turpentine is then cooled back to 20.0C, how far below the cylinders rim does the turpentines surface recede?arrow_forwardIn Figure P19.22, the change in internal energy of a gas that is taken from A to C along the blue path is +800 J. The work done on the gas along the red path ABC is 500 J. (a) How much energy must be added to the system by heat as it goes from A through B to C? (b) If the pressure at point A is five times that of point C, what is the work done on the system in going from C to D? Figure P19.22 (c) What is the energy exchanged with the surroundings by heat as the gas goes from C to A along the green path? (d) If the change in internal energy in going from point D to point A is +500 J, how much energy must be added to the system by heat as it goes from point C to point D?arrow_forwardThe rectangular plate shown in Figure P16.60 has an area Ai equal to w. If the temperature increases by T, each dimension increases according to Equation 16.4, where is the average coefficient of linear expansion. (a) Show that the increase in area is A = 2Ai T. (b) What approximation does this expression assume?arrow_forward
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