Temperature and kinetic theory
Temperature is average molecular kinetic energy, heat is energy in transit, and the ideal gas law ties the two pictures together.
Absolute temperature
Temperature measures the average kinetic energy of a substance's molecules; absolute zero (0 K = -273 C) is the floor where that motion is minimal. Kelvin and Celsius degrees are the same size, so T(K) = T(C) + 273. Only absolute temperature may be multiplied or divided in gas formulas — ratios of Celsius readings are meaningless.
T(\text{K}) = T(^\circ\text{C}) + 273Gas law and speed
The ideal gas law PV = nRT links pressure, volume, moles, and absolute temperature, with R = 8.31 J/(mol K). Kinetic theory goes further: the rms molecular speed is v = sqrt(3RT/M), where M is molar mass in kilograms per mole. Hotter means faster, heavier means slower — nitrogen at room temperature averages roughly 500 m/s.
v_{rms} = \sqrt{\frac{3RT}{M}}Worked example
How much heat raises 0.40 kg of aluminum from 25 C to 55 C? Aluminum's specific heat is 900 J/(kg K), so Q = mc*delta-T = (0.40)(900)(30) = 10,800 J. The same 10,800 J poured into 0.40 kg of water (c = 4186) would warm it only about 6.5 C, showing how much more energy water soaks up per degree.
Q = mc\Delta T = (0.40)(900)(30) = 1.08\times 10^4\ \text{J}Flashcard
Ideal gas law
Check your understanding
1.5 mol of an ideal gas sits at 400 K and a pressure of 200 kPa. What volume does it occupy?