Irodov Problem 2.22
Physics · fluid-mechanics · thermodynamics
Problem
One mole of nitrogen is contained in a vessel of volume V = = 1.00 1. Find: (a) the temperature of the nitrogen at which the pressure can be calculated from an ideal gas law with an error = 10% (as compared with the pressure calculated from the Van der Waals equation of state); (b) the gas pressure at this temperature.Intuitive explanation
The Van der Waals equation accounts for molecular volume and intermolecular attractions that the ideal gas law ignores—these corrections become significant at high pressures or low temperatures. Your task is to find the temperature where these real-gas effects create a 10% discrepancy between the two models, then calculate the actual pressure using Van der Waals. The key is setting up the ratio of pressures from both equations and solving for when that ratio equals 1.10.
Intuitive explanation
The Van der Waals equation accounts for molecular volume and intermolecular attractions that the ideal gas law ignores—these corrections become significant at high pressures or low temperatures. Your task is to find the temperature where these real-gas effects create a 10% discrepancy between the two models, then calculate the actual pressure using Van der Waals. The key is setting up the ratio of pressures from both equations and solving for when that ratio equals 1.10.