The gas equation for one mole of oxygen relates its pressure, $P$ (in atmospheres), its temperature, $T$ (in K), and its volume, $V$ (in cubic decimeters, dm${}^3$): $$T = 16.574\cdot{1 \over V} - 0.52754\cdot{1 \over V^2} - 0.3879\,P + 12.187\,V\,P.$$

(a) Find the temperature $T$ and differential $dT$ if the volume is 24 dm${}^3$ and the pressure is 1.5 atmosphere.
$T =$
$dT =$

(b) Use your answer to part (a) to estimate how much the volume would have to change if the pressure increased by 0.2 atmosphere and the temperature remained constant.
change in volume =