Q. A cylinder of fixed capacity $44.8\ litre$ contains a monoatomic gas at standard temperature and pressure. The amount of heat required to cylinder by $10℃$ will be ($R$ = universal gas constant)
A) $R$
B) $10R$
C) $20R$
D) $30R$
Explanation
(d) As we know $1\ mol$ of any ideal gas at $STP$ occupies a volume of $22.4\ litres.$
Hence number of moles of gas $\mu = \frac{44.8}{22.4} = 2$
Since the volume of cylinder is fixed,
Hence $(\mathrm{\Delta}Q)_{V} = \mu C_{V}\ \mathrm{\Delta}T$
$= 2 \times \frac{3}{2}R \times 10 = 30R\ \ \left\lbrack \because\left( C_{V} \right)_{mono} = \frac{3}{2}R \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.