To solve this problem, we can use Charles's Law, which states that the volume of a fixed mass of gas is directly proportional to its temperature, assuming constant pressure.
Charles's Law can be expressed as:
V1 / T1 = V2 / T2
Where: V1 is the initial volume T1 is the initial temperature (in Kelvin) V2 is the final volume (which we need to find) T2 is the final temperature (in Kelvin)
Let's convert the temperatures from Celsius to Kelvin:
T1 = 12°C + 273.15 = 285.15 K T2 = 100°C + 273.15 = 373.15 K
We know that V1 = 1 m^3 = 1000000 cm^3. Now we can rearrange the equation and solve for V2:
V2 = (V1 * T2) / T1 = (1000000 cm^3 * 373.15 K) / 285.15 K
Calculating this, we get:
V2 ≈ 1311921 cm^3
Therefore, when the temperature is increased from 12°C to 100°C at constant pressure, the volume of the gas will be approximately 1,311,921 cubic centimeters (cm^3).