At STP, 4.0 g of helium occupies a volume of 22400 cm ^3 . Given that the specific heat capacity of helium at constant pressure is 5.0 cal K ⁻¹ mol ⁻¹ , determine the speed of sound in helium at STP.

Step-by-step solution

Given mass of helium, m = 4.0 g = 4.0 10⁻³ kg Volume at STP, V = 22400 cm ^3 = 22.4 10⁻³ m ^3 Density of helium, = m V = 4.0 10⁻³ 22.4 10⁻³ = 1 5.6 kg m ⁻³ Molar heat capacity at constant pressure, C_p = 5.0 cal K ⁻¹ mol ⁻¹ Universal gas constant, R 2.0 cal K ⁻¹ mol ⁻¹ Molar heat capacity at constant volume, C_v = C_p - R = 5.0 - 2.0 = 3.0 cal K ⁻¹ mol ⁻¹ Ratio of specific heats, = C_p C_v = 5 3 Pressure at STP, P = 1.013 10^5 N m ⁻² The speed of sound in a gas is given by Laplace's formula: v = P Substituting the