Question

H calories of heat are required to raise the temperature of 1 mole of a monoatomic gas from ${200}^{o}C$ to ${300}^{o}C$ at constant volume. The amount of heat required (in calories) to raise the temperature of 2 moles of a diatomic gas from ${200}^{o}C$ to ${250}^{o}C$ at constant pressure is

• A. $\left(\frac{4}{3}\right)H$
• B. $\left(\frac{5}{3}\right)H$
• C. $2H$
• D. $\left(\frac{7}{3}\right)H$

Answer 1

The correct option is D $\left(\frac{7}{3}\right)H$

Heat required to rise the temperature at constant volume
$H=n{C}_v\Delta t$
$H=1\times \frac{3}{2}R\times 100=150R$
Heat required to rise the temperature at constant pressure
$H^{\prime }=n{C}_P\Delta T$
$H^{\prime }=2\times \frac{7}{2}R\times 50=350R$
$H^{\prime }=\frac{7}{3}H$