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  4. 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 °C ? (R = 8.31 J mol-1 K-1)

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Q. 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 $15\,{}^{\circ}C$ ?
$(R = 8.31\, J \,mol^{-1}\, K^{-1})$

Kinetic Theory

Solution:

Since one mole of any ideal gas at $STP$ occupies a volume of $22.4$ litre.
Therefore, cylinder of fixed capacity $44.8$ litre must contain $2$ moles of helium at $STP$.
For helium, $C_{V} = \frac{3}{2} R$ (monatomic)
$\therefore \quad$ Heat needed to raise the temperature,
$Q =$ number of moles $\times$ molar specific heat $\times$ raise in temperature
$= 2 \times \frac{3}{2} R \times 15 = 45R = 45\times 8.31\,J = 373.95\,J$