Question

The isothermal elasticity of a gas is equal to its.

• A. Final pressure
• B. Density
• C. Volume
• D. Specific heat

Answer 1

Answer: (A)

Final pressure

The isothermal elasticity is given by
$E_{iso}=\frac{volumestress}{volumestrain}=\frac{\Delta p}{-\frac{\Delta V}{V}}$ $[\because \Delta p=\frac{F}{A}]$
$\Rightarrow E_{iso}=-V\left(\frac{\Delta p}{\Delta V}\right)$.
Minus sign indicates decrease in volume due to increase in pressure.
From ideal gas equation
$pV=RT$
At constant temperature
$pV=$ constant
$\therefore p\Delta V+V\Delta p=0$
$\therefore V\left(\frac{\Delta p}{\Delta V}\right)=-p$
$\therefore E_{iso}=-V\left(\frac{-\Delta p}{\Delta V}\right)=-(-p)=p$
$=$ Final pressure.