Q 11-12-006NEETNEET 2023Top questionMedium
The temperature of a gas is $-50°$ C. To what temperature the gas should be heated so that the rms speed is increased by $3$ times?
Answer: (B) $3295°$ C
Concept. $v_{\text{rms}} \propto \sqrt{T}$.
Step 1. New speed. "Increased by 3 times" means $v + 3v = 4v$, so $T_2 = 16T_1$.
Step 2. Temperature.
$$T_2 = 16 \times 223 = 3568\ \text{K} = 3295°\text{C}$$
(Reading the new speed as $3v$ gives $2007$ K, which is not an option.)
Answer. $3295°$C (Option B).
Solution by Sreeraj P, M.Sc Physics