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 [2016]

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Q.
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 [2016]

1 Compressing the gas isothermally or adiabatically will require the same amount of work.

2 Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.

3 Compressing the gas isothermally will require more work to be done.

4 Compressing the gas through adiabatic process will require more work to be done.

Ans.
(4)

$V_{1} = V, V_{2} = V / 2$

On P–V diagram, Area under adiabatic curve > Area under isothermal curve.
So, compressing the gas through adiabatic process will require more work to be done.

Solution

Q.
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 [2016]

1 Compressing the gas isothermally or adiabatically will require the same amount of work.

2 Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.

3 Compressing the gas isothermally will require more work to be done.

4 Compressing the gas through adiabatic process will require more work to be done.

Ans.
(4)

$V_{1} = V, V_{2} = V / 2$

On P–V diagram, Area under adiabatic curve > Area under isothermal curve.
So, compressing the gas through adiabatic process will require more work to be done.

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Solution

Q. 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 [2016]

1 Compressing the gas isothermally or adiabatically will require the same amount of work.

2 Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.

3 Compressing the gas isothermally will require more work to be done.

4 Compressing the gas through adiabatic process will require more work to be done.

Ans. (4) V1=V, V2=V/2 On P–V diagram, Area under adiabatic curve > Area under isothermal curve. So, compressing the gas through adiabatic process will require more work to be done.

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Q.
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 [2016]

Ans.
(4)

$V_{1} = V, V_{2} = V / 2$

On P–V diagram, Area under adiabatic curve > Area under isothermal curve.
So, compressing the gas through adiabatic process will require more work to be done.