Question

For an adiabatic expansion of an ideal gas the fractional change in its pressure is equal to

Answer 1

in adiabatic process, Heat or mass doesn't flow from system to surrounding , or you can say that in adiabatic process heat or mass remains constant.

relation between pressure and volume in case of adiabatic process is given by ,
$PV^{\gamma}=K$
where P is pressure , V is volume , $\gamma$ is atomicity and k is constant.

now , differentiate both sides,
we get, $d(PV^{\gamma})=dK$

$V^{\gamma}dP+\gamma.PV^{\gamma-1}dV=0$

$V^{\gamma}dP=-\gamma.PV^{\gamma-1}dV$

$\frac{dP}{P}=-\frac{V^{\gamma-1}}{V^{\gamma}}\gamma.dV\\\\\frac{dP}{P}=-\gamma\frac{dV}{V}$

hence, fractional change in pressure equals to $-\gamma\times\text{fractional change in volume}$