To determine the temperature at which the volume of a gas triples while keeping the pressure constant, we can use Charles's law, which states that the volume of a given amount of gas is directly proportional to its temperature in Kelvin, assuming constant pressure. The equation for Charles's law is:
V₁ / T₁ = V₂ / T₂
Where: V₁ is the initial volume of the gas T₁ is the initial temperature of the gas in Kelvin V₂ is the final volume of the gas (triple the initial volume) T₂ is the final temperature of the gas in Kelvin
Given that the initial temperature is -127°C, we need to convert it to Kelvin by adding 273.15:
T₁ = -127°C + 273.15 = 146.15 K
Since the final volume is triple the initial volume, V₂ = 3V₁.
Substituting these values into the equation:
(3V₁) / T₂ = V₁ / T₁
Cross-multiplying and simplifying:
3V₁T₁ = V₁T₂
Dividing both sides by V₁:
3T₁ = T₂
Substituting the value of T₁:
3 * 146.15 K = T₂
T₂ ≈ 438.45 K
Therefore, at a temperature of approximately 438.45 Kelvin (or approximately 165.3°C), the volume of the gas would triple, assuming constant pressure.