Speed of sound at the same temperature will be maximum in

The speed of sound in an ideal gas depends on temperature and the gas's molar mass: v = √(γRT/M), where γ is the adiabatic index, R is the universal gas constant, T is the absolute temperature, and M is the molar mass of the gas. At the same temperature, a lower molar mass M gives a higher speed of sound, for gases with a similar γ.

1. Diatomic gases H2, N2, and O2 all have γ ≈ 1.4, so at the same temperature T, comparing v is equivalent to comparing 1/√M.

2. Molar masses: M(H2) ≈ 2 g/mol, M(N2) ≈ 28 g/mol, M(O2) ≈ 32 g/mol.

3. Since 2 < 28 < 32, it follows that 1/√2 > 1/√28 > 1/√32, so v(H₂) > v(N₂) > v(O₂) at the same temperature.

4. The option stating equal speed in all gases does not hold here, because M differs across H₂, N₂, and O₂, and v depends on M.

Measured speeds of sound at 0°C (273 K) approximate this trend: about 1270 m/s in hydrogen, about 334 m/s in nitrogen, and about 317 m/s in oxygen — hydrogen's value is far higher, consistent with its much smaller molar mass.

So, at the same temperature, the speed of sound is maximum in H2 gas.