MCAT content library / Chemistry & physics / Gas particles, heat capacity, and nonideality
Use a molecular model to explain gas pressure, temperature, heat capacity, and why real gases deviate from ideal behavior.
About 18 minutes, including pressure–volume curves and constant-volume versus constant-pressure heating.
Useful foundations
Temperature tracks average molecular kinetic energy
In the ideal-gas model, particles move randomly, occupy negligible volume, and interact through elastic collisions rather than long-range attractions or repulsions. Gas pressure arises from collisions with container walls.
For an ideal gas, the average translational kinetic energy per molecule is proportional to absolute temperature. At the same temperature, molecules of different masses have the same average translational kinetic energy even though the lighter molecules have greater average speed.
Heating at constant pressure requires more energy than heating at constant volume
At constant volume, a heated gas cannot expand against an external pressure, so no pressure–volume expansion work is done. At constant pressure, heating usually causes expansion, so some supplied energy leaves the gas as work on the surroundings.
For the same temperature increase in an ideal gas, the molar heat capacity at constant pressure therefore exceeds the heat capacity at constant volume: Cp > Cv.
Worked application: fixed container versus movable piston
An original experiment heats equal amounts of the same ideal gas from 300 K to 350 K.
| Condition | Volume | Expansion work | Heat required for same ΔT |
|---|---|---|---|
| Rigid container | Constant | 0 | Lower |
| Movable piston at constant external pressure | Increases | Positive work done by gas | Higher |
The internal-energy change for the same ideal gas and same temperature change depends only on temperature, but the constant-pressure process also requires energy for expansion work. That is why more heat must be supplied.
Real gases deviate for two different physical reasons
Real particles have finite size and intermolecular attractions. At moderate density, attractive forces can pull molecules back from the wall and reduce measured pressure relative to an ideal prediction. At very high density, finite molecular size and short-range repulsion become important, reducing the free volume available for motion and tending to raise pressure relative to the simplest ideal model.
The van der Waals equation summarizes these corrections in one common model:
(P + a n²/V²)(V − nb) = nRT
The a term represents attractive interactions; the b term accounts for excluded volume. The equation is a useful correction model, not a perfect description under every condition.
Worked pattern: read the direction of deviation
| Condition | Observed pressure versus ideal | Most plausible dominant effect |
|---|---|---|
| Moderate pressure, strong attractions | Lower | Attractive forces reduce wall-collision pressure |
| Very high density | Higher | Excluded volume/short-range repulsion dominate |
| Low pressure, high temperature | Near ideal | Interactions and particle volume matter less |
ACTIVE PRACTICE · GAS HEATING
Compare Rigid and Movable Containers at the Same Temperature Change
The original model heats equal amounts of one ideal gas from 300 K to 350 K. A rigid container does no expansion work; a movable piston under constant pressure expands and does positive work. To compute a numerical example, use the additional stipulated model of 0.100 mol ideal monatomic gas with CV,m = 3R/2, CP,m = 5R/2 and R = 8.314 J mol⁻¹ K⁻¹.
Rigid-container heat: . Piston heat: . Work by the expanding gas: .
The numerical heat capacities are additional simplifying assumptions for the interactive monatomic ideal-gas example; the original lesson provides the qualitative comparison. Heat and work signs use work done by gas as positive.
Check your reasoning
Choose an answer before opening its feedback.
Check 1
A real gas has lower pressure than the ideal-gas prediction at the same n, V, and T. Which molecular effect most plausibly dominates?
A. Attractive intermolecular forces
Correct. Attractions reduce the effective momentum transfer to the walls relative to the ideal model.
B. Excluded volume alone
Review this choice. Excluded volume tends to increase pressure at high density.
C. Molecules have zero kinetic energy.
Review this choice. The gas is at nonzero temperature.
D. The gas contains no particles.
Review this choice. n is fixed and nonzero.
Check 2
Helium and nitrogen gas are at the same absolute temperature. Which statement about average translational kinetic energy is correct in the ideal-gas model?
A. They have the same average translational kinetic energy per molecule.
Correct. Average translational kinetic energy depends on temperature, not molecular mass.
B. Helium must have more average translational kinetic energy because it moves faster.
Review this choice. Its lower mass gives higher typical speed at the same average kinetic energy.
C. Nitrogen must have twice the kinetic energy.
Review this choice. Molecular mass does not set average translational kinetic energy at fixed temperature.
D. Both have zero kinetic energy.
Review this choice. Nonzero temperature implies molecular motion.
Check 3
Equal amounts of the same ideal gas are heated through the same temperature increase, once at constant volume and once at constant pressure. Why is more heat required at constant pressure?
A. The gas also does expansion work on the surroundings.
Correct. The supplied energy must cover both the internal-energy increase and pressure–volume work.
B. The gas has a lower final temperature.
Review this choice. The temperature change is specified as the same.
C. Constant-volume heating destroys particles.
Review this choice. Particle number is unchanged.
D. Work is always zero at constant pressure.
Review this choice. Expansion at constant pressure generally involves nonzero work.