Specifically heated

Classical Mechanics Level 3

An ideal gas C P C V = γ \frac { { C }_{ P } }{ { C }_{ V } } =\gamma is taken through a process in which pressure and volume vary as P = a V B P=a{ V }^{ B } { "a" is a constant }. Find the value of "B" for which the molar specific heat capacity of gas in this process is z e r o zero

γ \gamma − γ -\gamma R − γ R-\gamma a γ γ − 1 \frac { a\gamma }{ \gamma -1 } R a − γ \frac { R }{ a } -\gamma a γ R − 1 \frac { a\gamma }{ R-1 } a γ a γ − 1 \frac { a\gamma }{ a\gamma -1 } a R a γ − 1 \frac { aR }{ a\gamma -1 }

Jaswinder Singh by Jaswinder Singh , 23, India

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1 solution

Jaswinder Singh
Feb 21, 2016

Δ Q = n C Δ T \Delta Q=nC\Delta T Δ U = n C V Δ T \Delta U={ nC }_{ V }\Delta T W = n R Δ T B + 1 W=\frac { nR\Delta T }{ B+1 } Δ Q = Δ U + W \Delta Q=\Delta U+W C Δ T = C V Δ T + R Δ T B + 1 C\Delta T={ C }_{ V }\Delta T+\frac { R\Delta T }{ B+1 } 0 = R γ − 1 + R B + 1 0=\frac { R }{ \gamma -1 } +\frac { R }{ B+1 } B = − γ B=-\gamma

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