NapkinCalc

Thermodynamics — Energy & Cycles

The ideal gas law — pressure, volume, temperature

continues from lesson 2 — values defined earlier in the course stay live here

ELI5: for a gas, P·V = m·R·T ties pressure, volume, mass, and temperature into one equation — squeeze it, heat it, and the others respond. Here R is the specific gas constant (287 J/kg·K for air). With units on, the engine keeps pascals, cubic metres, kilograms and kelvin straight automatically.

mair:=0.0283kgm_{air} := 0.0283 kg = 0.0283 kg mass of air in the box
Rair:=287J/(kg∗K)R_{air} := 287 J/(kg*K) = 287 J / (kg K) specific gas constant for air
Tgas:=300KT_{gas} := 300 K = 300 K room temperature
Vgas:=0.024m3V_{gas} := 0.024 m^3 = 0.024 m^3 24 litres
Pgas:=mair∗Rair∗Tgas/VgasinkPaP_{gas} := m_{air} * R_{air} * T_{gas} / V_{gas} in kPa = 101.53 kPa pressure ≈ 101 kPa — about one atmosphere
✓ pass abs(Pgas−101.5kPa)<2kPaabs(P_{gas} - 101.5 kPa) < 2 kPa that much air in 24 L at room temperature sits at ~1 atm