A sound wave travels twice as far in neon (Ne) as it does it krypton (Kr) in the same time interval. Both neon and krypton can be treated as monatomic ideal gases. The atomic mass of neon is 20.2 u, and that of krypton is 83.8 u. The temperature of the krypton is 292 K. What is the temperature of the neon

281.6 K

Explanation:

The speed of sound in an ideal gas is given by c = √(γKT/m).

From the question speed of sound in Ne, c₁ = 2c₂ speed of sound in Kr

c₁ = √(γKT₁/m₁) and c₂ = √(γKT₂/m₂)

So  √(γKT₁/m₁)  = 2√(γKT₂/m₂) where T₁, m₁ and T₂, m₂ are the temperatures and atomic masses of Neon and Krypton respectively.

So, √(T₁/m₁)  = 2√(T₂/m₂)

(T₁/m₁)  = 4(T₂/m₂) (squaring both sides)

T₁ = 4(T₂m₁/m₂)

Given that m₁ = 20.2 u , m₂ = 83.8 u, T₂ = 292 K

T₁ = 4(292 × 20.2/83.8) K = 23593.6/83.8 = 281.55 K ≅ 281.6 K

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