Example

Question:

A cylinder of fixed capacity 44.8 litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by 15.0°C? (\(R = 8.31\,\mathrm{J\,mol^{-1}\,K^{-1}}\))

Solution:

At STP, 1 mole of ideal gas occupies 22.4 litres, so 44.8 litres contains 2 moles of helium.
For a monatomic gas (helium), molar specific heat at constant volume is \[ C_v = \frac{3}{2}R \] Since the volume is fixed, use \(C_v\).
Heat required:
\(\text{Heat required} = \text{no. of moles} \times \text{molar specific heat} \times \text{rise in temperature}\) \[ Q = 2 \times 1.5R \times 15.0 = 45R \] \[ Q = 45 \times 8.31 = 374\,\mathrm{J} \]