Physics · Thermal Properties Of Matter · NEET
Always Kelvin. The T in PV = nRT is the absolute temperature. If a question gives you degrees Celsius, first convert using T(K) = t(Celsius) + 273.15 (use 273 in NEET unless told otherwise). Putting Celsius directly is the most common mistake, and it breaks badly near low temperatures because Celsius can be zero or negative while absolute temperature never is.
Start from PV = nRT. In this thermometer the volume V is held constant and the amount of gas n is fixed, so n, R and V are all constants. That leaves P = (nR/V) T, meaning P is directly proportional to T. So if you measure the pressure of the trapped gas, you directly know its absolute temperature. This is why the pressure-versus-temperature graph is a straight line through the origin (in Kelvin).
They mean the same thing: the number of moles of gas. NCERT uses the Greek letter mu, and most other books use n. Number of moles = mass of gas divided by its molar mass, or number of molecules divided by Avogadro number. Do not confuse mu here with anything else; in this equation it is simply moles.
For a constant-volume gas thermometer, P is proportional to absolute temperature T. If you plot pressure against Celsius temperature you get a straight line, and extending (extrapolating) that line down, the pressure would become zero at minus 273.15 degrees Celsius. Real gases liquefy before this, but the maths says pressure cannot go below zero, so this point is the lowest possible temperature. That is absolute zero, which is 0 K.
Yes. NCERT points out that since PV = constant (Boyle's law at fixed T) and V/T = constant (Charles' law at fixed P) for a given amount of gas, the combination PV/T must also be constant. So for the same gas going from state 1 to state 2: P1 V1 / T1 = P2 V2 / T2. This combined form is very useful in numericals when two of the three quantities change.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
R = 8.31 J per mol per K (NCERT value). In other units it is about 0.0821 litre-atmosphere per mol per K. Use 8.31 when the pressure and volume are in SI units (pascal and cubic metre).
The trapped gas is kept at a fixed volume by adjusting a mercury column, so its volume never changes. Because volume is constant, only pressure changes with temperature, and pressure directly tells you the absolute temperature.
Gas laws describe proportionality (P proportional to T, V proportional to T). Proportionality only works on a scale where zero means zero motion of molecules. Celsius zero is just the freezing point of water, so ratios in Celsius give wrong answers. The Kelvin scale starts at absolute zero, so proportional gas laws hold true.
For a fixed amount of gas, P1 V1 / T1 = P2 V2 / T2, with all temperatures in Kelvin. This comes directly from PV/T being constant, and it lets you solve problems where pressure, volume and temperature all change between two states.
