Question

The adiabatic and isothermal volume elasticities $E_{\varphi }$ and $E_{\theta }$ of a gas, are related as

• A. $\frac{E_{\varphi }}{E_{\theta }}=\gamma$
• B. $\frac{E_{\theta }}{E_{\varphi }}=\gamma$
• C. $E_{\varphi }-E_{\theta }=\gamma$
• D. $E_{\theta }-E_{\varphi }=\gamma$

Answer 1

The correct option is A $\frac{E_{\varphi }}{E_{\theta }}=\gamma$

Volume elasticity is defined as
$E=-V\left(\frac{dP}{dV}\right)$
so $E_{iso}=P$ ( from $PV=constant$)
and $E_{adi}=\gamma P$ (from $P{V}^{\gamma }=constant$)
so, $\frac{E_{adi}}{E_{iso}}=\gamma$