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#4: A cylinder with a piston contains 0.250 mol of oxygen at 2.40x10^5 Pa and 3 K. The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally, it is cooled isochorically to its original pressure. Show the series of processes in a PV diagram. 6) Compute the temperature during the isothermal compression. Compute the maximum pressure. Compute the work done by the gas, the heat added to it, and its internal energy change during the initial expansion. Compute the work done by the gas, the heat added to it, and its internal energy change during the final cooling. Compute the work done by the gas, the heat added to it, and its internal energy change during the isothermal compression. For oxygen, Cv = 20.85 J/mol K, Cp = 29.17 J/mol K, and γ = 1.4.

          #4: A cylinder with a piston contains 0.250 mol of oxygen at 2.40x10^5 Pa and 3 K. The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally, it is cooled isochorically to its original pressure.

Show the series of processes in a PV diagram.

6) Compute the temperature during the isothermal compression. Compute the maximum pressure. Compute the work done by the gas, the heat added to it, and its internal energy change during the initial expansion. Compute the work done by the gas, the heat added to it, and its internal energy change during the final cooling. Compute the work done by the gas, the heat added to it, and its internal energy change during the isothermal compression.

For oxygen, Cv = 20.85 J/mol K, Cp = 29.17 J/mol K, and γ = 1.4.

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Added by Brooke W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Sri K

08/02/2023

Step 1

PV diagram: The first process is an isobaric expansion, so the volume doubles while the pressure remains constant at 2.40x10^5 Pa. This is represented by a horizontal line on the PV diagram. The second process is an isothenal compression, so the volume decreases Show more…

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#4: A cylinder with a piston contains 0.250 mol of oxygen at 2.40x10^5 Pa and 3 K. The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally, it is cooled isochorically to its original pressure. Show the series of processes in a PV diagram. 6) Compute the temperature during the isothermal compression. Compute the maximum pressure. Compute the work done by the gas, the heat added to it, and its internal energy change during the initial expansion. Compute the work done by the gas, the heat added to it, and its internal energy change during the final cooling. Compute the work done by the gas, the heat added to it, and its internal energy change during the isothermal compression. For oxygen, Cv = 20.85 J/mol K, Cp = 29.17 J/mol K, and γ = 1.4.

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Transcript

00:01 So, in this question it is given to draw the pv diagram.

00:12 So, let us be the y -axis and this be the x -axis.

00:18 X -axis is the volume and y -axis is the pressure.

00:24 This is a point a and this is a point b and this is the point c.

00:34 The direction of flow is represented by arrows.

00:38 This curve is known as p directly proportional to 1 divided by v that is isothermal and this curve is where p equals to constant and this is isobaric and this curve is when the v is a constant and this is known as isochoric.

01:22 Now it is given to find the equations for temperature.

01:27 So, for the process ab which is an isobaric process we can write that v is directly proportional to t that is v naught divided by t1 is equals to 2 v naught divided by tb that is tb is equals to 2t1 which is equal to 2 multiplied with 355.

02:04 So, from this we get the value of tb is equal to 710 kelvin.

02:15 Since it is deduced from the figure that the process bc is an isothermal process.

02:30 So, we can say that the temperature of b is equal to temperature of c that is 710 kelvin.

02:38 Proceeding further for the third part it is given that for process bc we can write pv is equals to constant that is pbvb is equal to pcvc that is p1 multiplied with 2 v naught is equal to p2 multiplied with v naught.

03:16 Substituting the values we can get p2 is equal to 2 multiplied with 2 .4 multiplied with 10 to the power 5 that is the value of p2 is equal to 4 .8 multiplied with 10 to the power 5 pascal...

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