A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:
compressing the gas through an adiabatic process will require more work to be done.
compressing the gas isothermally or adiabatically will require the same amount of work to be done.
which of the case (whether compression through isothermal or through the adiabatic process) requires more work to be done will depend upon the atomicity of the gas.
compressing the gas isothermally will require more work to be done.
During compression from a given initial volume to a smaller final volume, the pressure increases. In an adiabatic compression, the temperature also increases, which causes the pressure to rise more steeply compared to an isothermal compression where the temperature remains constant. On a - indicator diagram, the adiabatic curve lies above the isothermal curve for compression. Since the magnitude of work done on the gas is equal to the area under the - curve, the area under the adiabatic curve is greater. Therefore, more work is required for adiabatic compression than for isothermal compression.
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