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Starting with the same inital conditions, an ideal gas expands from volume V1 to V2 in three different ways. The work done by the gas is W1 if the process is isothermal, W2 if isobaric and W3 if adiabatic, then
- a)W2 > W1 >W3
- b)W2 >W3 > W1
- c)W1 > W2 > W3
- d)W1 > W3 > W2
Correct answer is option 'A'. Can you explain this answer?
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Starting with the same inital conditions, an ideal gas expands from vo...
We cannot determine the exact values of W1, W2, and W3 without knowing the pressure and temperature conditions of the gas. However, we can make some general observations about the work done in each process based on the type of process and the initial and final volumes.
Isothermal process:
In an isothermal process, the temperature of the gas remains constant. This means that the pressure must decrease as the volume increases in order to maintain the same temperature. The work done by the gas in an isothermal process is given by:
W1 = nRT ln(V2/V1)
where n is the number of moles of gas, R is the gas constant, and T is the temperature of the gas. Since ln(V2/V1) is always greater than zero (since V2>V1), we know that W1 is always positive. This means that the gas is doing work on its surroundings in an isothermal expansion.
Isobaric process:
In an isobaric process, the pressure of the gas remains constant. This means that the gas can expand freely without doing any work against the pressure. The work done by the gas in an isobaric process is given by:
W2 = P(V2 - V1)
where P is the constant pressure of the gas. Since V2>V1, we know that W2 is always positive. This means that the gas is doing work on its surroundings in an isobaric expansion.
Adiabatic process:
In an adiabatic process, no heat is exchanged between the gas and its surroundings. This means that the temperature and pressure of the gas will change as it expands. The work done by the gas in an adiabatic process is given by:
W3 = (P2V2 - P1V1)/(γ - 1)
where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and γ is the ratio of specific heats for the gas. Since the adiabatic process is not specified as either an expansion or a compression, we cannot determine the sign of W3 without knowing the specific conditions.
Overall, we can say that W2 is always positive and represents work done by the gas on its surroundings in an isobaric expansion. The signs of W1 and W3 depend on the specific conditions of the gas and the process.
Isothermal process:
In an isothermal process, the temperature of the gas remains constant. This means that the pressure must decrease as the volume increases in order to maintain the same temperature. The work done by the gas in an isothermal process is given by:
W1 = nRT ln(V2/V1)
where n is the number of moles of gas, R is the gas constant, and T is the temperature of the gas. Since ln(V2/V1) is always greater than zero (since V2>V1), we know that W1 is always positive. This means that the gas is doing work on its surroundings in an isothermal expansion.
Isobaric process:
In an isobaric process, the pressure of the gas remains constant. This means that the gas can expand freely without doing any work against the pressure. The work done by the gas in an isobaric process is given by:
W2 = P(V2 - V1)
where P is the constant pressure of the gas. Since V2>V1, we know that W2 is always positive. This means that the gas is doing work on its surroundings in an isobaric expansion.
Adiabatic process:
In an adiabatic process, no heat is exchanged between the gas and its surroundings. This means that the temperature and pressure of the gas will change as it expands. The work done by the gas in an adiabatic process is given by:
W3 = (P2V2 - P1V1)/(γ - 1)
where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and γ is the ratio of specific heats for the gas. Since the adiabatic process is not specified as either an expansion or a compression, we cannot determine the sign of W3 without knowing the specific conditions.
Overall, we can say that W2 is always positive and represents work done by the gas on its surroundings in an isobaric expansion. The signs of W1 and W3 depend on the specific conditions of the gas and the process.
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Starting with the same inital conditions, an ideal gas expands from volume V1to V2in threedifferent ways. The work done by the gas is W1 if the process is isothermal, W2if isobaric and W3if adiabatic, thena)W2 > W1 >W3b)W2 >W3 >W1c)W1 > W2 > W3d)W1 > W3> W2Correct answer is option 'A'. Can you explain this answer?
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