JEE MAIN - Physics (2021 - 18th March Evening Shift - No. 14)
For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $$\gamma$$ is the ratio of specific heats) :
$$ - {1 \over \gamma }{{dV} \over V}$$
$$ - \gamma {V \over {dV}}$$
$$ - \gamma {{dV} \over V}$$
$${{dV} \over V}$$
คำอธิบาย
for adiabatic expansion :
PV$$\gamma$$ = const.
$$ \Rightarrow $$ ln P + $$\gamma$$ln v = const.
$$ \Rightarrow $$ differentiating both sides;
$${{dp} \over p} + \gamma {{dv} \over v} = 0$$
$$ \Rightarrow {{dp} \over p} = - \gamma {{dv} \over V}$$
PV$$\gamma$$ = const.
$$ \Rightarrow $$ ln P + $$\gamma$$ln v = const.
$$ \Rightarrow $$ differentiating both sides;
$${{dp} \over p} + \gamma {{dv} \over v} = 0$$
$$ \Rightarrow {{dp} \over p} = - \gamma {{dv} \over V}$$