At what temperature the gas density will be 1.5 times its density at 100 degrees Celsius. The pressure is considered constant.
Given: ρ2 (final gas density) = 1.5ρ1 (initial gas density); Т1 (initial gas temperature) = 100 ºС (absolute temperature Т1 = 373 К).
To determine the desired gas temperature, we use the ideal gas equation of state: P * V = m / M * R * T; P = m / (V * M) * R * T = ρ / M * R * T, whence ρ1 / M * R * T1 = ρ2 / M * R * T2; T2 = ρ1 * T1 / ρ2 = T1 / 1.5.
Calculation: T2 = 373 / 1.5 = 248.7 K (-24.3 ºС).
Answer: The density of the gas will reach the required value at a temperature of -24.3 ºС.
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