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Answer :
To calculate the decrease in temperature when 6.00 L at 20.0 °C is compressed to 4.00 L, we need to use the ideal gas law, PV = nRT.
How do you calculate temperature drop due to pressure drop?
- You subtract the final temperature from the starting temperature to find the difference. So if something starts at 50 degrees Celsius and finishes at 75 degrees C, then the change in temperature is 75 degrees C – 50 degrees C = 25 degrees C. For decreases in temperature, the result is negative.
- Use the formula: k = T1/P1. For example, if a gas at an initial temperature of 300 K and an initial pressure of 100 Pa, drops by 50 Pa, the proportionality constant k = 3 K/Pa = 300/100 = T1/P1. Multiply the drop in pressure by the proportionality constant k to obtain the drop in temperature.
- First, we need to convert the temperature from Celsius to Kelvin: 20.0 °C + 273.15 = 293.15 K
- Next, we need to find the initial pressure, using the ideal gas law: P1V1 = nRT, where P1 = initial pressure, V1 = initial volume, n = number of moles, R = ideal gas constant, T = temperature in Kelvin.
- We know that V1 = 6.00 L, T = 293.15 K, and R = 8.314 J/mol·K. We do not know the value of n, so we can assume it is 1 mole. Therefore, P1 = (nRT) / V1 = (1 x 8.314 x 293.15) / 6.00 = 476.89 J/L
- Finally, we can calculate the final pressure, using the same equation: P2V2 = nRT, where P2 = final pressure, V2 = final volume. We know that V2 = 4.00 L, T = 293.15 K, and R = 8.314 J/mol·K. Substituting these values into the equation, we get P2 = (nRT) / V2 = (1 x 8.314 x 293.15) / 4.00 = 715.34 J/L
- To find the decrease in temperature, we subtract the final pressure from the initial pressure: P1 - P2 = 476.89 J/L - 715.34 J/L = -238.45 J/L
- So the decrease in temperature when 6.00 L at 20.0 °C is compressed to 4.00 L is -238.45 J/L.
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Final answer:
By applying Charles's law, the decrease in temperature when 6.00 L at 20.0 °C is compressed to 4.00 L is found to be approximately 97.72 °C.
Explanation:
To calculate the decrease in temperature when 6.00 L at 20.0 °C is compressed to 4.00 L, we'll need to apply Charles's law. This law states that for a constant amount of gas at a constant pressure, the volume of the gas is directly proportional to its temperature.
First, convert the initial temperature from degrees Celsius to Kelvin using the conversion formula: Kelvin = Celsius + 273.15, which results to 293.15 K. Let's denote the initial volume and temperature as V₁ and T₁, and the final volume and unknown temperature as V₂ and T₂, respectively.
According to Charles's law, V₁/T₁ = V₂/T₂. By substituting the known values: (6.00 L)/293.15 K = (4.00 L)/T₂. Simplifying this equation gives us T₂ = [(4.00 L) * 293.15 K]/6.00 L = 195.43 K. Convert this back to Celsius, resulting in -77.72 °C. The decrease in temperature is therefore 20.0°C - (-77.72 °C) = 97.72 °C
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