<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<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.">
<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.">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<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> alex@savchenkosolutions.com <br></small>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<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.">
<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.">
<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.">
<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.">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<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.">
<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>
<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> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
