What is the relationship between the isotherm | vedclass

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(B) The isothermal bulk modulus is defined as $E_	heta = -V (dP/dV)_	heta = P$.For an adiabatic process,$PV^\gamma = 	ext{constant}$.Differentiatin

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$E_\phi = \gamma E_	heta$

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(B) The isothermal bulk modulus is defined as $E_	heta = -V (dP/dV)_	heta = P$.For an adiabatic process,$PV^\gamma = 	ext{constant}$.Differentiating with respect to $V$,we get $P(\gamma V^{\gamma-1}) + V^\gamma (dP/dV) = 0$.This simplifies to $dP/dV = -\gamma P/V$.The adiabatic bulk modulus is $E_\phi = -V (dP/dV)_\phi = -V(-\gamma P/V) = \gamma P$.Since $E_	heta = P$,we substitute to get $E_\phi = \gamma E_	heta$.

What is the relationship between the isothermal bulk modulus $E_\theta$ and the adiabatic bulk modulus $E_\phi$? (where $\gamma = C_p/C_v$)

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