Question

A certain amount of an ideal monoatomic gas needs $20J$ of heat energy to raise its temperature by ${10}^{o}C$ at constant pressure. The heat needed for the same temperature rise at constant volume will be:

• A. $30J$
• B. $12J$
• C. $200J$
• D. $215.3J$

Answer 1

The correct option is B $12J$

$Q_P=n{C}_P\Delta T$

$Q_V=n{C}_v\Delta T$

$\therefore \frac{Q_P}{Q_V}=\frac{n{C}_P\Delta T}{n{C}_V\Delta T}$

$\Rightarrow \frac{20}{Q_V}=\frac{C_P}{C_V}[\because Q_P=20J]$

As we know that,

$\frac{C_P}{C_V}=\frac{5}{3}$

$\therefore \frac{20}{Q_V}=\frac{5}{3}$

$\Rightarrow Q_V=12J$

Hence the heat needed for the same temperature rise at constant volume will be $12J$.