Ideal gas: understanding PV = nRT
The ideal-gas model links pressure, volume, amount of substance and absolute temperature. It is very useful but remains an approximation.
The essential idea
The ideal-gas model links pressure, volume, amount of substance and absolute temperature. It is very useful but remains an approximation.
Example
At fixed amount and volume, increasing absolute temperature increases pressure in the ideal model.
Mini problem
Why must kelvins be used in PV = nRT?
Show the solution
Answer: Because the equation uses absolute temperature, whose zero corresponds to thermodynamic zero.
Explanation: At fixed volume and amount of gas, what happens to pressure when absolute temperature rises from 300 K to 600 K? At fixed amount and volume, increasing absolute temperature increases pressure in the ideal model.
Method: Connect the definition to the mechanism described in the lesson: identify what changes and what remains fixed before drawing the conclusion.
Common mistake
Do not replace reasoning with a memorized rule. Always check geometry, units, coefficients or model assumptions.
Guided exercise
At fixed volume and amount of gas, what happens to pressure when absolute temperature rises from 300 K to 600 K?
Show the detailed solution
Answer: In the ideal model, P is proportional to T under these conditions. Doubling T therefore doubles pressure.
Explanation: At fixed amount and volume, increasing absolute temperature increases pressure in the ideal model. The ideal-gas model links pressure, volume, amount of substance and absolute temperature.
Method: Connect the definition to the mechanism described in the lesson: identify what changes and what remains fixed before drawing the conclusion.
Avoid this
Do not substitute 27 °C for 300 K in a temperature ratio: gas laws use absolute temperature.