Physics · Thermodynamics · NEET
A state variable is a property that describes the condition of the gas right now, when it is in thermal equilibrium. Pressure P, volume V, temperature T, internal energy U, and number of moles n are state variables. If you know these, you know the state of the gas. You do not need to know its past. Think of it like a photo: the photo shows where the gas is now, not the road it took to get there.
A state variable depends only on the present state (P, V, T, U). A path variable depends on the route taken between two states. Heat (Q) and work (W) are path variables, not state variables. Example: the same gas can go from state 1 to state 2 by an isothermal path or an adiabatic path, and Q and W will be different for each path, but the change in a state variable like U is the same. Rule to remember: P, V, T, U are state variables; Q and W are NOT.
The equation of state is the fixed relation that connects the state variables of a system. For an ideal gas it is PV = nRT, where R = 8.31 J per mol per kelvin. It is called the equation of state because it lets you fix the whole state using fewer numbers. Since PV = nRT ties P, V, T together, only two of them are free to choose. Pick any two, and the third is fixed. This is why a P-V graph (or P-T, or V-T) can show every possible state.
Extensive variables depend on the amount (size or mass) of the system. If you double the gas, they double. Examples: volume V, internal energy U, total mass, number of moles n, total heat capacity. Intensive variables do NOT depend on amount. If you split the gas into two halves, each half has the same value. Examples: pressure P, temperature T, density, specific heat. Quick test: cut the system in half. If the quantity halves, it is extensive; if it stays the same, it is intensive.
Both temperature T and pressure P are intensive. If you take a box of gas at 300 K and 1 atm and split it into two boxes, each box is still at 300 K and 1 atm. The amount changed but T and P did not. Volume V is extensive because each half has half the volume. A handy trick: an intensive variable divided into an extensive one gives an intensive ratio, for example V (extensive) / n (extensive) = molar volume (intensive).
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Only two independent state variables are needed for a fixed amount of gas, because the equation of state PV = nRT links P, V and T. Choose any two and the third is decided. That is why a single point on a P-V graph fixes the whole state.
Yes. Internal energy U is a state variable, and for an ideal gas it depends only on temperature. So the change in U between two states is the same for every path, even though Q and W differ from path to path.
Density is intensive. It is mass divided by volume, both extensive, and the ratio does not depend on the amount of gas. Splitting the gas leaves the density unchanged.
PV = nRT is exact only for an ideal gas. Real gases follow it closely at low pressure and high temperature. At high pressure or low temperature, corrections (like van der Waals terms) are needed, but for NEET the ideal-gas equation of state is used.
Because their values depend on the path taken between two states, not just on the start and end states. The same change of state can happen with different amounts of heat and work, so neither can be a property of the state itself.
