Concept explainers
A cylinder that has a 40.0-cm radius and is 50.0 cm deep is filled with air at 20.0°C and 1.00 atm (Fig. P10.74a). A 20.0-kg piston is now lowered into the cylinder, compressing the air trapped inside as it takes equilibrium height hi (Fig. P16.74b). Finally, a 25.0-kg dog stands on the piston, further compressing the air, which remains at 20°C (Fig. P16.74c). (a) How far down (Δh) does the piston move when the dog steps onto it? (b) To what temperature should the gas be warmed to raise the piston and dog back to hi?
(a)
The height which the piston moves down when the dog steps onto the piston.
Answer to Problem 74P
The height at which the piston move down when the dog steps onto the piston is
Explanation of Solution
Write the expression for Boyle’s law, for the initial and final state since the temperature is constant.
Here,
Use
Here,
When the piston moves down, then the external pressure on the piston is
Equate the equation (II) with the equation
Replace the mass
Here,
The piston moves downward when the dog steps on the piston. It can be expressed as,
Use equation (III) and (IV) in (V).
Conclusion:
Substitute,
Therefore, the height at which the piston move down when the dog steps onto the piston is
(b)
The temperature at which the gas should be warmed to raise the piston and dog back to
Answer to Problem 74P
The temperature at which the gas should be warmed to raise the piston and dog back to
Explanation of Solution
Write the expression for Charles’s law, for the initial and final state since the pressure is constant.
Here,
Use
Use equation (III) and (IV) in the equation (VIII).
Conclusion:
Substitute,
Therefore, The temperature at which the gas should be warmed to raise the piston and dog back to
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Chapter 16 Solutions
Principles of Physics: A Calculus-Based Text
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