Q. One mole of an ideal monoatomic gas requires $210\ J$ heat to raise the temperature by $10K,$ when heated at constant temperature. If the same gas is heated at constant volume to raise the temperature by $10K$ then heat required is
A) $238\ J$
B) $126\ J$
C) $210\ J$
D) $350\ J$
Explanation
(b) $(\mathrm{\Delta}Q)_{P} = \mu C_{P}\mathrm{\Delta}T$ and $(\mathrm{\Delta}Q)_{V} = \mu C_{V}\mathrm{\Delta}T$
$\Rightarrow \frac{(\mathrm{\Delta}Q)_{V}}{(\mathrm{\Delta}Q)_{P}} = \frac{C_{V}}{C_{P}} = \frac{\frac{3}{2}R}{\frac{5}{2}R} = 3/5$
$\left\lbrack \because\left( C_{V} \right)_{mono} = \frac{3}{2}R,\left( C_{P} \right)_{mono} = \frac{5}{2}R \right\rbrack$
$\Rightarrow (\mathrm{\Delta}Q)_{V} = \frac{3}{5} \times (\mathrm{\Delta}Q)_{P} = \frac{3}{5} \times 210 = 126\ J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.