Question

4.0g of a gas occupies 22.4liters at NTP. The specific heat capacity of the gas at constant volume is 5.0JK–1mol–1. If the speed of sound in this gas at NTP is 952ms–1, then the heat capacity at constant pressure is (Take gas constant R=8.3JK–1mol–1)

Answer 1

Answer:

Explanation:

Since 4.0 g of a gas occupies 22.4 litres at NTP, thus the molecular mass of the gas is M = 4.0 g mol-1

Speed of the sound in the gas is = v = √γRT/M

where γ is the ratio of two specific heats, R is the universal gas constant and T is the temperature of the gas. Thus

= γ = Mv²/RT

= γ = 4.0 ×10`³

v = 952ms`1, R = 8.3 Kmol`1 and T = 273K

= γ = 4.0 ×10`³ × 952ms`1, / 8.3 Kmol`1 × 273K

= 1.6

= γ = Cp/Cv or Cp = = γCv

Thus,

= 1.6 ×  5.0JK–1mol–1

= 8.0JK

Thus, the heat capacity at constant pressure is 8.0JK.

Answer 2

Explanation:

As the molecular weight of the gas is 4 gm. So it will be He gas, a monoatomic gas.

Gammma for monoatomic gas is 1.6

So the Cp value = 1.6×5 = 8 j/k mol