The temperature of a gas is −50°C. To what temperature should the gas be heated so that the RMS speed is increased by 3 times?

Question

G1 Physics · Accepted Answer

Step 1: RMS speed obeys vRMS = √(3RT/M), hence vRMS ∝ √T for a fixed gas. Step 2: Initial absolute temperature T₁ = −50 + 273 = 223 K. Step 3: In the book’s use of “increased by 3 times”, the speed increases by 3v and becomes v₂ = v₁ + 3v₁ = 4v₁. Step 4: T₂/T₁ = (v₂/v₁)² = 4² = 16. Step 5: T₂ = 16 × 223 = 3568 K = 3295°C. Final answer: (D) 3295°C.