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<meta name="description" content="In a rarefied space, a cylindrical container remains vertically, covered at the top by a movable piston of mass M. Inside the closed volume, there is a monoatomic gas at temperature T and pressure P. The interior cross-section of the cylinder is S, the height of volume where gas lies is H. The piston is set free and is moved. What maximum speed will develope the piston, if gas is compressed by the piston a) isothermally and b) adiabatically? The acceleration due to gravity is g.">
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<meta property="og:description" content="In a rarefied space, a cylindrical container remains vertically, covered at the top by a movable piston of mass M. Inside the closed volume, there is a monoatomic gas at temperature T and pressure P. The interior cross-section of the cylinder is S, the height of volume where gas lies is H. The piston is set free and is moved. What maximum speed will develope the piston, if gas is compressed by the piston a) isothermally and b) adiabatically? The acceleration due to gravity is g.">
<title>In a rarefied space, a cylindrical container remains vertically, covered at the top by a movable piston of mass M. Inside the closed volume, there is a monoatomic gas at temperature T and pressure P. The interior cross-section of the cylinder is S, the height of volume where gas lies is H. The piston is set free and is moved. What maximum speed will develope the piston, if gas is compressed by the piston a) isothermally and b) adiabatically? The acceleration due to gravity is g.</title>
In a rarefied space, a cylindrical container remains vertically, covered at the top by a movable piston of mass $M$. Inside the closed volume, there is a monoatomic gas at temperature $T$ and pressure $P$. The interior cross-section of the cylinder is $S$, the height of volume where gas lies is $H$. The piston is set free and is moved. What maximum speed will develope the piston, if gas is compressed by the piston a) isothermally and b) adiabatically? The acceleration due to gravity is $g$.
</p>
<center>
<figure>
<img src="statement.png"
loading="lazy" alt="1.1.1" width="150" />
<figcaption>
For the 5.6.22 problem
</figcaption>
</figure>
</center>
<h3>Solution</h3>
<p>
a) From Energy Conservation Law or Kinetic Energy - Work theorem
$$\frac{Mv^2}{2} = Mg(H-y) + A \;(1)$$
where $A$ is the work done over the piston, equals to work done by gas, in this case (isothermal process) defined by
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
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<meta name="description" content="The largest dataset of solutions of 'Savchenko. Problems in Physics'. Savchenko’s Problems in General Physics is widely used to prepare for olympiads and it is a useful tool to
<meta name="description" content="In a rarefied space, a cylindrical container remains vertically, covered at the top by a movable piston of mass M. Inside the closed volume, there is a monoatomic gas at temperature T and pressure P. The interior cross-section of the cylinder is S, the height of volume where gas lies is H. The piston is set free and is moved. What maximum speed will develope the piston, if gas is compressed by the piston a) isothermally and b) adiabatically? The acceleration due to gravity is g.">
master and sharpen your skills and techniques in comptetitive problem solving. Some of these problems were a source
of inspiration for Jaan Kalda’s handouts and to some NBPhO problems. You may find problems from old IPhO
<meta property="og:title" content="In a rarefied space, a cylindrical container remains vertically, covered at the top by a movable piston of mass M. Inside the closed volume, there is a monoatomic gas at temperature T and pressure P. The interior cross-section of the cylinder is S, the height of volume where gas lies is H. The piston is set free and is moved. What maximum speed will develope the piston, if gas is compressed by the piston a) isothermally and b) adiabatically? The acceleration due to gravity is g.">
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<meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook">
<meta property="og:description" content="In a rarefied space, a cylindrical container remains vertically, covered at the top by a movable piston of mass M. Inside the closed volume, there is a monoatomic gas at temperature T and pressure P. The interior cross-section of the cylinder is S, the height of volume where gas lies is H. The piston is set free and is moved. What maximum speed will develope the piston, if gas is compressed by the piston a) isothermally and b) adiabatically? The acceleration due to gravity is g.">
<title>In a rarefied space, a cylindrical container remains vertically, covered at the top by a movable piston of mass M. Inside the closed volume, there is a monoatomic gas at temperature T and pressure P. The interior cross-section of the cylinder is S, the height of volume where gas lies is H. The piston is set free and is moved. What maximum speed will develope the piston, if gas is compressed by the piston a) isothermally and b) adiabatically? The acceleration due to gravity is g.</title>
In a rarefied space, a cylindrical container remains vertically, covered at the top by a movable piston of mass $M$. Inside the closed volume, there is a monoatomic gas at temperature $T$ and pressure $P$. The interior cross-section of the cylinder is $S$, the height of volume where gas lies is $H$. The piston is set free and is moved. What maximum speed will develope the piston, if gas is compressed by the piston a) isothermally and b) adiabatically? The acceleration due to gravity is $g$.
In a rarefied space, a cylindrical container remains vertically, covered at the top by a movable piston of mass $M$. Inside the closed volume, there is a monoatomic gas at temperature $T$ and pressure $P$. The interior cross-section of the cylinder is $S$, the height of volume where gas lies is $H$. The piston is set free and is moved. What maximum speed will develope the piston, if gas is compressed by the piston a) isothermally and b) adiabatically? The acceleration due to gravity is $g$.
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" alt="1.1.1" width="150" />
loading="lazy" alt="1.1.1" width="150" />
<figcaption>
<figcaption>
For the 5.6.22 problem
For the 5.6.22 problem
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
a) From Energy Conservation Law or Kinetic Energy - Work theorem
a) From Energy Conservation Law or Kinetic Energy - Work theorem
$$\frac{Mv^2}{2} = Mg(H-y) + A \;(1)$$
$$\frac{Mv^2}{2} = Mg(H-y) + A \;(1)$$
where $A$ is the work done over the piston, equals to work done by gas, in this case (isothermal process) defined by
where $A$ is the work done over the piston, equals to work done by gas, in this case (isothermal process) defined by
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
