To solve this problem, you can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, given constant pressure.
1. First, calculate the initial volume of the gas at 135°C:
V1 = 100.0 L
2. Then, convert the temperatures to Kelvin by adding 273.15 to the Celsius temperatures:
Initial temperature (T1) = 135°C + 273.15 = 408.15 K
Final temperature (T2) = 72.0°C + 273.15 = 345.15 K
3. Next, use Charles's Law to find the final volume (V2) at 72.0°C:
V1 / T1 = V2 / T2
4. Substitute the known values into the formula:
100.0 L / 408.15 K = V2 / 345.15 K
5. Rearrange the formula to solve for V2:
V2 = (100.0 L * 345.15 K) / 408.15 K
6. Calculate the final volume of the gas at 72.0°C:
V2 = (100.0 * 345.15) / 408.15 ≈ 84.35 L
Therefore, the volume of the gas when its temperature decreases to 72.0°C is approximately 84.35 L.
