To find the new volume of the gas, we can use the combined gas law equation, which relates the initial and final states of the gas.
The combined gas law equation is given by:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure = 1 atm
V1 = initial volume = 22.4 L
T1 = initial temperature in Kelvin = 10 + 273 = 283 K
P2 = final pressure = 2 atm
T2 = final temperature in Kelvin = 100 + 273 = 373 K
V2 = final volume (what we want to find)
Substituting the given values into the equation:
(1 * 22.4) / 283 = (2 * V2) / 373
Simplifying the equation:
22.4 / 283 = 2V2 / 373
To isolate V2, we cross-multiply:
2V2 = (22.4 / 283) * 373
Dividing both sides by 2:
V2 = (22.4 / 283) * 373 / 2
Calculating the value:
V2 ≈ 29.8 L
Therefore, the new volume of the gas, when the temperature increases to 100°C and the pressure increases to 2 atm, is approximately 29.8 liters.