Q. The temperature of the mixture of one mole of helium and one mole of hydrogen is increased from $0℃$ to $100℃$ at constant pressure. The amount of heat delivered will be
A) $600\ cal$
B) $1200\ cal$
C) $1800\ cal$
D) $3600\ cal$
Explanation
(b) $\left( C_{P} \right)_{mix} = \frac{\mu_{1}C_{P_{1}} + \mu_{2}C_{P_{2}}}{\mu_{1} + \mu_{2}}(C_{P_{1}}(He) = \frac{5}{2}R\ and\ C_{P_{2}}\left( H_{2} \right) = \frac{7}{2}R)$
$= \frac{1 \times \frac{5}{2}R + 1 \times \frac{7}{2}R}{1 + 1} = 3R = 3 \times 2 = 6cal/mol.℃$
$\therefore$ Amount of heat needed to raise the temperature from $0℃$ to $100℃$
$(\mathrm{\Delta}Q)_{P} = \mu C_{P}\mathrm{\Delta}T = 2 \times 6 \times 100 = 1200\ cal$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.