Question

The temperature of the mixture of one mole of helium and one more of hydrogen is increased from $0^{o}C$ to ${100}^{o}C$ at constant pressure. The amount of heat delivered will be

• A. $600cal$
• B. $1200cal$
• C. $1800cal$
• D. $3600cal$

Answer 1

Answer: (B)

$1200cal$

$(C_P{)}_{mix}$ = $\frac{{\mu }_1{C}_{P1}+{\mu }_2{C}_{P2}}{{\mu }_1+\mu 2}$
($C_{P_1}\left(He\right)$ = $\frac{5}{2}R$ and $C_{P_2}\left(H_2\right)$ = $\frac{7}{2}R$)
$(C_P{)}_{mix}=\frac{1\times \frac{5}{2}R+1\times \frac{7}{2}R}{1+1}$
$=3R\times 2$ = $6cal/mo{l}^o.C$
$\therefore$ Amount of heat needed to raise the temperature from $0^{o}C$ to ${100}^{o}C$
$(△Q{)}_P$ = $\mu C_P△T$ = $2\times 6\times 100$ = $1200cal$