question_answer

The volume of an ideal gas is V at pressure P. On increasing the pressure by \[\Delta P\], the change in volume of the gas is \[\Delta {{V}_{1}}\] under isothermal conditions and \[\Delta {{V}_{2}}\] under adiabatic conditions. Under which of the two conditions, will the change in volume be more? Given reason.

Answer:

                Under isothermal conditions, the bulk modulus of elasticity is \[{{K}_{iso}}=\frac{\Delta P}{\Delta {{V}_{1}}/V}=P\]                                      ... (i) Under adiabatic conditions, the bulk modulus  of elasticity is \[{{K}_{adia}}=\frac{\Delta P}{\Delta {{V}_{2}}/V}=\gamma P\]                                  ?(ii) Dividing (ii) by (i), we get \[\frac{\Delta {{V}_{1}}}{\Delta {{V}_{2}}}=\gamma \] As \[\gamma >1,\]so \[\Delta {{V}_{1}}>\Delta {{V}_{2}}\]