To what temperature should the hydrogen at room temperature (27^∘ C) be heated at constant press

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To what temperature should the hydrogen at room temperature...

To what temperature should the hydrogen at room temperature $\left(27^{\circ} \mathrm{C}\right)$ be heated at constant pressure so that the rms velocity of its molecule becomes double of its previous value (A) $927^{\circ} \mathrm{C}$ (B) $600^{\circ} \mathrm{C}$ (C) $108^{\circ} \mathrm{C}$ (D) $1200^{\circ} \mathrm{C}$

To what temperature should the hydrogen at room temperature $\left(27^{\circ} \mathrm{C}\right)$ be heated at constant pressure so that the rms velocity of its molecule becomes double of its previous value
(A) $927^{\circ} \mathrm{C}$
(B) $600^{\circ} \mathrm{C}$
(C) $108^{\circ} \mathrm{C}$
(D) $1200^{\circ} \mathrm{C}$

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Key Concepts

Kinetic Theory of Gases

Kinetic theory explains that the molecules of a gas are in constant motion and that the average kinetic energy of these molecules is directly proportional to the absolute temperature. This principle underpins the relationship between temperature and molecular speeds, highlighting why an increase in temperature leads to higher average kinetic energy.

Root Mean Square (rms) Speed

The root mean square speed of gas molecules is a statistical measure of their speed, defined by the formula v_rms = ?(3kT/m) for an ideal gas. This shows that the rms speed is proportional to the square root of the temperature, meaning that if the rms speed is doubled, the absolute temperature must be increased by a factor of four.

Temperature Conversion

Temperature must be expressed in an absolute scale (Kelvin) when applying kinetic theory formulas because these formulas are derived based on absolute temperature. Converting from degrees Celsius to Kelvin by adding 273 (approximately 273.15 for more precision) is essential to correctly compute changes in kinetic parameters.

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