cylinder, a piston is let free to move so that the gas slowly expands in such a way that its pressure s directly proportional to its volume. After the gas reaches the volume 3V and pressure 3p, the piston is pushed in so that the gas is compressed isobarically to its original volume V. The gas is then cooled isochorically until it returns to the original volume and pressure. Find the work W done on the gas during the entire process. VISUALIZE Show the process on a pV diagram. Note whether it happens to be one of the basic gas processes: isochoric, isobaric, or isothermal. SOLVE Calculate the work as the area under the pv curve either geometrically or by carrying out the integration: work done on the gas W =- pdv--(area under pV curve) REVIEW Check your signs. W> 0 when the gas is compressed. Energy is transferred from the environment to the gas. when the ynands Energy is transferred from the nas to the environmen

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Find the amount of work W done on the gas during the entire process.
Express your answer in terms of some or all of the variables p and V.
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W =
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Transcribed Image Text:Find the amount of work W done on the gas during the entire process. Express your answer in terms of some or all of the variables p and V. ▸ View Available Hint(s) W = Submit ΑΣΦ Request Answer SE ?
A cylinder with initial volume V contains a sample of a gas at pressure p. On one end of the
cylinder, piston is let free to move so that the gas slowly expands in such a way that its pressure
is directly proportional to its volume. After the gas reaches the volume 3V and pressure 3p, the
piston is pushed in so that the gas is compressed isobarically to its original volume V. The gas is
then cooled isochorically until it returns to the original volume and pressure.
Find the work W done on the gas during the entire process.
VISUALIZE Show the process on a pV diagram. Note whether it happens to be one of the basic gas processes: isochoric, isobaric, or isothermal.
SOLVE Calculate the work as the area under the pV curve either geometrically or by carrying out the integration:
work done on the gas W
REVIEW Check your signs.
W> 0 when the gas is compressed. Energy is transferred from the environment to the gas.
• W <0 when the gas expands. Energy is transferred from the gas to the environment.
• No work done if the volume doesn't change, W=0.
– Svip dV = -(area under pV curve)
Transcribed Image Text:A cylinder with initial volume V contains a sample of a gas at pressure p. On one end of the cylinder, piston is let free to move so that the gas slowly expands in such a way that its pressure is directly proportional to its volume. After the gas reaches the volume 3V and pressure 3p, the piston is pushed in so that the gas is compressed isobarically to its original volume V. The gas is then cooled isochorically until it returns to the original volume and pressure. Find the work W done on the gas during the entire process. VISUALIZE Show the process on a pV diagram. Note whether it happens to be one of the basic gas processes: isochoric, isobaric, or isothermal. SOLVE Calculate the work as the area under the pV curve either geometrically or by carrying out the integration: work done on the gas W REVIEW Check your signs. W> 0 when the gas is compressed. Energy is transferred from the environment to the gas. • W <0 when the gas expands. Energy is transferred from the gas to the environment. • No work done if the volume doesn't change, W=0. – Svip dV = -(area under pV curve)
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