To solve this problem, we can use Charles' Law, which states that the volume of a gas is directly proportional to its temperature when pressure and the amount of gas are held constant.
The formula for Charles' Law is:
V1 / T1 = V2 / T2
Where: V1 is the initial volume T1 is the initial temperature V2 is the final volume (what we want to find) T2 is the final temperature
Given: V1 = 1 m³ (1 cubic centimeter is equivalent to 1 x 10^-6 cubic meters) T1 = 12 °C + 273.15 (converted to Kelvin) T2 = 100 °C + 273.15 (converted to Kelvin)
Substituting the values into the formula, we have:
1 m³ / (12 °C + 273.15 K) = V2 / (100 °C + 273.15 K)
Simplifying the equation:
1 / 285.15 K = V2 / 373.15 K
Cross-multiplying:
V2 = (1 / 285.15 K) * 373.15 K V2 ≈ 1.308 m³
Therefore, when the temperature is increased to 100 °C, the volume of the gas will be approximately 1.308 m³.