Final answer:
The new volume of the helium when cooled from 27°C to -78°C at constant pressure is calculated using Charles's Law, which results in a final volume of 73.98 L.
Step-by-step explanation:
To calculate the new volume of helium when cooled from 27 degrees Celsius to -78 degrees Celsius at a constant pressure, we can use Charles's Law. Charles's Law states that for a given mass of gas at constant pressure, the volume is directly proportional to its temperature in kelvins (V/T = k). Therefore, we need to convert our temperatures to kelvins and solve for the final volume.
Initial temperature (T1): 27°C = 27 + 273.15 = 300.15 K
Initial volume (V1): 113 L
Final temperature (T2): -78°C = -78 + 273.15 = 195.15 K
Using the formula V1/T1 = V2/T2, we can rearrange to solve for the final volume (V2):
V2 = (V1 × T2) / T1
Plugging in our values, we get:
V2 = (113 L × 195.15 K) / 300.15 K
V2 = 22204.95 L·K / 300.15 K
V2 = 73.98 L (rounded to two decimal places)
The new volume of the helium when cooled to -78°C at a constant pressure is 73.98 L.