Answer:
This problem can be solved using the ideal gas law:
PV = nRT
where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in Kelvin.
First, we need to convert the initial temperature of 20.0 °C to Kelvin:
T1 = 20.0 + 273.15 = 293.15 K
Next, we can assume that the number of moles of gas and the pressure remain constant throughout the compression process. Therefore, we can rearrange the ideal gas law to solve for the final temperature:
T2 = (P1V1/T1) * V2
where P1 is the initial pressure, V1 is the initial volume, and V2 is the final volume.
Since the problem does not provide information about the pressure or number of moles of gas, we can assume they are constant and cancel out of the equation:
T2 = (V2/V1) * T1
Plugging in the given values, we get:
T2 = (4.00 L / 6.00 L) * 293.15 K = 195.43 K
To find the decrease in temperature, we subtract the final temperature from the initial temperature:
ΔT = T1 - T2 = 293.15 K - 195.43 K = 97.72 K
Therefore, the temperature decreases by 97.72 K when 6.00 L at 20.0 °C is compressed to 4.00 L.