By applying Boyle's Law and assuming constant pressure, we were able to calculate that compressing the gas resulted in a decrease of 98.05 K in temperature. This highlights the interesting relationship between pressure, volume, and temperature in ideal gases.
Note:
This solution assumes ideal gas behavior, which may not be completely accurate for real gases.
The pressure is assumed to be constant, which might not be true in all compression scenarios.
When a gas is compressed, its temperature typically increases due to the work done on it. However, in this scenario, we're presented with the unusual situation where the volume is reduced but the temperature decreases. Let's delve into this phenomenon and calculate the temperature drop in Kelvin.
Given:
Initial volume (V1) = 3.00 mL
Initial temperature (T1) = 21°C = 294.15 K (converted from Celsius)
Final volume (V2) = 1.50 mL
Assumptions:
The gas behaves ideally, meaning it follows Boyle's Law.
The pressure remains constant during the compression.
Solution:
Boyle's Law: We can apply Boyle's Law, which states that for an ideal gas at constant temperature, the product of pressure and volume remains constant: P1 * V1 = P2 * V2.
Temperature Change: Since the pressure is assumed to be constant, the change in temperature is inversely proportional to the change in volume. Therefore, we can write: T1/V1 = T2/V2.
Solving for T2 (final temperature): Rearranging the equation for T2, we get: T2 = T1 * (V1/V2) = 294.15 K * (3.00 mL / 1.50 mL) = 196.10 K.
Temperature Decrease: Finally, to calculate the decrease in temperature, we simply subtract the final temperature from the initial temperature: 294.15 K - 196.10 K = 98.05 K.
Therefore, the decrease in temperature when 3.00 mL of gas at 21°C is compressed to 1.5 mL is 98.05 K.