A sample of gas expands from volume V1 to V2.The amount of work done b...
Explanation:
When a gas expands, the volume of the gas increases, and the gas performs work on its surroundings. The amount of work done by the gas during expansion depends on several factors, including the pressure, temperature, and nature of the expansion.
Isothermal Expansion:
In an isothermal expansion, the temperature of the gas remains constant, which means that the gas absorbs or releases heat to maintain its temperature. During this type of expansion, the pressure of the gas decreases as the volume increases, and the work done by the gas is given by the following equation:
W = nRT ln(V2/V1)
where W is the work done by the gas, n is the amount of gas, R is the gas constant, T is the temperature of the gas, V1 is the initial volume of the gas, and V2 is the final volume of the gas.
As the above equation shows, the work done by the gas during an isothermal expansion depends on the initial and final volumes of the gas, and is independent of the pressure or nature of the expansion. Therefore, the amount of work done by the gas is greatest during an isothermal expansion.
Isobaric and Adiabatic Expansion:
In an isobaric expansion, the pressure of the gas remains constant, and the work done by the gas is given by the following equation:
W = P (V2 - V1)
where P is the constant pressure of the gas.
In an adiabatic expansion, the gas expands without exchanging heat with its surroundings, and the work done by the gas is given by the following equation:
W = (γ / (γ - 1)) P (V2 - V1)
where γ is the ratio of specific heats.
As the above equations show, the work done by the gas during an isobaric or adiabatic expansion depends on the pressure and volume of the gas, and is independent of the nature of the expansion. Therefore, the amount of work done by the gas is less during an isobaric or adiabatic expansion compared to an isothermal expansion.
Conclusion:
In conclusion, the correct option is 'A' because the amount of work done by the gas is greatest during an isothermal expansion, where the temperature of the gas remains constant.
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