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Question

An ideal gas has initial volume V and pressure p. If the volume of gas is doubled during expansion, then minimum work will be done in which thermodynamic process ?
  1. Isobaric process 
  2. Isothermal process 
  3. Adiabatic process 
  4. Same in all alone given process 


Solution

The correct option is C Adiabatic process 
Wgas=P dV
Hence work done by gas in each process can be compared by estimating the area under their respective PV graphs. 


Plotting the PV curve for the given isobaric, isothermal, adiabatic processes for expansion of gas from V2V.
slopeAdiabatic>slopeIsothermal
Hence, curve of adiabatic process will be more steep compared to that of isothermal one.

we get the following order for area under curve:
AIsobaric>AIsothermal>AAdiabatic
WIsobaric>WIsothermal>WAdiabatic
Hence, minimum work is done by gas in adiabatic process.

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