RMS Speed Shortcut – NEET/JEE

Full transcript

Let's solve this classic RMS speed question using a simple and powerful shortcut that will save you precious time in NEET and JEE exams. The RMS speed formula is the square root of 3RT over M. When two gases have equal RMS speeds, we can set their ratios equal, giving us the key relationship that temperature is directly proportional to molar mass. Oxygen has a molar mass of 32 grams per mole and hydrogen has 2 grams per mole, making oxygen exactly sixteen times heavier. So for equal RMS speeds, oxygen's absolute temperature must also be sixteen times greater than hydrogen's. The temperature of oxygen is given as 47 degrees Celsius. We must always convert to Kelvin when using kinetic theory formulas, so we add 273 to get exactly 320 Kelvin. Dividing 320 Kelvin by 16 gives us 20 Kelvin for hydrogen. Converting back to Celsius by subtracting 273 gives us negative 253 degrees Celsius, which we box as our final answer. The correct answer is option two, negative 253 degrees Celsius. Remember this NEET and JEE shortcut: when RMS speeds are equal, temperature divided by molar mass is always constant for both gases. Keep practicing with KritaMCQs!