Q. 6

Can a process on an ideal gas be both adiabatic and isothermal?

Answer :


According to the first law of thermodynamics,


dQ = dU + dW = nCvdT + dW … (i),


where


dQ = heat supplied


dU = change in internal energy


dW = work done on the gas


n= number of moles


Cv = specific heat capacity at constant volume


dT = change in temperature


For an adiabatic process, dQ(heat supplied) = 0.


An adiabatic process occurs without the transfer of heat or mass of substances between the thermodynamic system and the surrounding.


For an isothermal process, dT(change in temperature) = 0


An Isothermal process is a change of system, in which the temperature remains constant ∆T=0.


Putting these values in (i), we get


dW = 0,


which is not possible for either of the processes.


dW = 0 only in the case of a process where the volume is constant that is dV = 0,


since dW = PdV,


where P = pressure and dV = change in volume.


Hence, we conclude that a process cannot be both adiabatic and isothermal.


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