To calculate the decrease in temperature when a gas is compressed, we need to assume that the process is adiabatic (no heat exchange with the surroundings) and that the gas follows the ideal gas law. In an adiabatic process, the change in temperature is related to the change in volume by the following equation:
(T1 / T2) = (V2 / V1)^((γ - 1) / γ)
Where: T1 = Initial temperature T2 = Final temperature V1 = Initial volume V2 = Final volume γ = Ratio of specific heats (for diatomic gases, such as oxygen and nitrogen, γ is approximately 1.4)
Let's plug in the given values into the equation:
T1 = 21 degrees Celsius = 21 + 273.15 = 294.15 K V1 = 2 L V2 = 1.00 L γ = 1.4
(T1 / T2) = (V2 / V1)^((γ - 1) / γ) T2 = T1 / (V2 / V1)^((γ - 1) / γ)
Substituting the values:
T2 = 294.15 K / (1.00 L / 2 L)^((1.4 - 1) / 1.4)
Calculating the expression in the parentheses:
T2 = 294.15 K / (0.5)^(0.4 / 1.4)
T2 ≈ 294.15 K / 0.857
T2 ≈ 342.44 K
To convert this temperature back to Celsius:
T2 ≈ 342.44 - 273.15
T2 ≈ 69.29 degrees Celsius
Therefore, the decrease in temperature when 2 liters at 21 degrees Celsius is compressed to 1.00 liter is approximately 21 degrees Celsius - 69.29 degrees Celsius = -48.29 degrees Celsius.