To determine the temperature at which the gas sample would increase its volume from 2L to 4L, we can use the combined gas law, which relates the initial and final conditions of the gas sample. The combined gas law equation is as follows:
(P₁V₁) / (T₁) = (P₂V₂) / (T₂)
Where: P₁ and P₂ are the initial and final pressures of the gas (assuming constant pressure), V₁ and V₂ are the initial and final volumes of the gas, T₁ and T₂ are the initial and final temperatures of the gas (measured in Kelvin).
In this case, we know that the initial volume (V₁) is 2L, and the final volume (V₂) is 4L. The initial temperature (T₁) is given as 0°C, which needs to be converted to Kelvin by adding 273.15 (0°C + 273.15 = 273.15 K). We need to find the final temperature (T₂).
Using the combined gas law, we can set up the equation as follows:
(2L * T₁) = (4L * T₂)
Substituting the known values:
(2L * 273.15 K) = (4L * T₂)
Simplifying the equation:
546.3 K = (4L * T₂)
To solve for T₂, we divide both sides of the equation by 4L:
T₂ = 546.3 K / (4L)
Calculating this gives us:
T₂ ≈ 136.575 K
Therefore, to increase the volume of the gas sample from 2L to 4L, the temperature should be approximately 136.575 K.