To solve this problem, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure is kept constant. The mathematical expression for Charles's Law is:
V1 / T1 = V2 / T2
Where: V1 = Initial volume of the gas T1 = Initial temperature of the gas (in Kelvin) V2 = Final volume of the gas (to be determined) T2 = Final temperature of the gas (in Kelvin)
Now, let's convert the given temperatures from Celsius to Kelvin by adding 273.15 to each temperature:
T1 = 12°C + 273.15 = 285.15 K T2 = 100°C + 273.15 = 373.15 K
We are given that the initial volume, V1, is 1 m^3 = 1,000,000 cm^3.
Now we can solve for V2:
V1 / T1 = V2 / T2
1,000,000 cm^3 / 285.15 K = V2 / 373.15 K
Cross-multiplying:
V2 = (1,000,000 cm^3 * 373.15 K) / 285.15 K V2 ≈ 1,313,863.58 cm^3
Therefore, when the temperature is increased to 100°C, the volume of the gas will be approximately 1,313,864 cm^3.