At what temperature was the ideal gas located if, upon cooling to a temperature
| September 2, 2021 | education
At what temperature was the ideal gas located if, upon cooling to a temperature of – 72 C, the root-mean-square velocity of its molecules halved?
Data: Т2 (final temperature of the taken gas) = -72 ºС (absolute temperature Т2 = 201 К); V1 (original root mean square velocity) = 2V2 (final root mean square velocity).
The initial temperature of the taken ideal gas is determined using the formula: V = √ (3 * R * T / M); V2 = 3 * R * T / M, where 3 * R / M = V1 ^ 2 / T1 = V2 ^ 2 / T2.
Calculation: V1 ^ 2 / T1 = V2 ^ 2 / T2.
(2V2) 2 / T1 = V2 ^ 2 / T2.
T1 = 4T2 = 4 * 201 = 804 K (531 ºС).
Answer: Before cooling, the taken ideal gas had a temperature of 531 ºС.
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