Question

A monoatomic ideal gas has an internal energy $1.5nRT$ . A cylinder has cross-section $9.055cm^{2}$ . It contains $2moles$ of $He$ gas. The cylinder is closed by a light frictionless piston. The gas is heated slowly in a process during which a total of $185.62J$ heat is given to the gas. If the temperature rises through $6^\circ C,$ find the distance moved by the piston (in $cm$ ). Consider atmospheric pressure to be $100kPa$ and universal gas constant $=8.3Jmol^{- 1}K^{- 1}$ .

Answer 1

$\Delta U=1.5nR\left(\right.\Delta T\left.\right)=1.5\left(\right.2\left.\right)\left(\right.8.3\left.\right)\left(\right.6\left.\right)=149.4J$
Heat given to the gas $=185.62J$
Work done by the gas is,
$\Delta W=\Delta Q-\Delta U=185.62-149.40$
$\therefore \Delta W=36.22J...\left(i\right)$
If the distance moved by the piston is $x$ , then work done is,
$\Delta W=PAx$
$\therefore 36.22=\left(10\right)^{5}\times 9.055\times \left(10\right)^{- 4}\times \left(\right.x\left.\right)$ ...[From equation $\left(i\right)$ ]
$\therefore x=\frac{36 . 22}{90 . 55}=\frac{18 . 11 \times 2}{18 . 11 \times 5}=\frac{2}{5}=0.4m=40cm$