A sample of an ideal gas contains 3.0 × 1022 molecules at 27 °C. What is the total random kinetic energy of its molecules?
- Change to kelvin: T = 27 + 273 = 300 K.
- Mean kinetic energy of one molecule = (3/2)kT = 1.5 × 1.38 × 10−23 × 300 = 6.21 × 10−21 J.
- Total = 3.0 × 1022 × 6.21 × 10−21 = 186 J.
- An ideal gas has no potential energy, so this is also its internal energy.
Answer: About 190 J.