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An ideal gas undergoes a quasistatic, reversible process in which its molar heat capacity C remains constant. It during this process the relation the pressure p and volume V is given by pV^n=constant, then n is given by (here C_p and C_v are molar specific heat at constant pressure and constant volume respectively).

Answer» <html><body><p>`n=C_p/C_v`<br/>`n=(<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>-C_p)/(C-C_v)`<br/>`n=(C_p-C)/(C-C_v)`<br/>`n=(C-C_v)/(C-C_p)`</p>Solution :Here `<a href="https://interviewquestions.tuteehub.com/tag/pv-593601" style="font-weight:bold;" target="_blank" title="Click to know more about PV">PV</a>^n=k` (constant)…….(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>) <br/> For 1 mol of ideal gas <br/> `pV=RT`……..(2) <br/> Dividing (1) by (2) we get `V^(n-1) T=k/R` <br/> `<a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a>((dV)/(dT))=V/((n-1)T)=V/((1-n)T)`<br/>According to first law of <a href="https://interviewquestions.tuteehub.com/tag/thermodynamics-12722" style="font-weight:bold;" target="_blank" title="Click to know more about THERMODYNAMICS">THERMODYNAMICS</a> <br/> `dQ=C_vdT+pdV`<br/> `therefore(dQ)/(dT)=C_V+p((dV)/(dT))=C_v+(pV)/((1-n)T)=C_v+R/(1-n)`<br/>Hence thermal capacity, `C=C_v+R/(1-n)` <br/> or,`1-n=R/(C-C_v)`<br/> or,`n=1-R/(C-C_v)=(C-(C_v-R))/(C-V_v)=(C-C_p)/(C-C_v)`[`because C_p-C_v=R`]</body></html>


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