Chemistry · Thermodynamics · NEET
Internal energy is the TOTAL energy stored inside a system. It is the sum of every kind of energy the particles have: their motion (kinetic energy of translation, rotation, vibration) and the energy stored in the bonds and forces between them (potential energy). We use the symbol U. When you heat a gas or do work on it, you change its internal energy. NCERT says U can be chemical, electrical, mechanical or any other type — the sum of all of them.
Internal energy is a STATE FUNCTION. This is one of the most tested ideas in NEET. A state function only depends on the current state of the system (its pressure, volume, temperature), not on the road you took to reach that state. Heat (q) and work (w) are path functions — they depend on the path. But their sum, ΔU = q + w, is always a state function.
Because U is a property of the system itself, it has one fixed value for one fixed state. Joule proved this by experiment: he changed water from state A to state B in two different ways — by doing mechanical work (churning with paddles) and by adding heat. No matter which path he used, the same starting and ending temperature gave the SAME change in internal energy. So ΔU = U(final) − U(initial) depends only on the two end states, which is exactly what 'state function' means.
No. ΔU does NOT depend on the path. This is the whole point of being a state function. You might do a lot of work along one path and add little heat, or add lots of heat and do little work along another path — but if the starting and ending states are the same, ΔU is identical. Only q and w change with the path; their sum stays fixed.
The formula is ΔU = q + w (the first law of thermodynamics). Here q is the heat given TO the system (positive if absorbed) and w is the work done ON the system (positive if work is done on the gas). ΔU = U(final) − U(initial). For an ideal gas, ΔU also equals nC(v)ΔT, so ΔU depends only on temperature change.
Yes. For an IDEAL gas, internal energy depends only on temperature. In an isothermal process the temperature is constant (ΔT = 0), so ΔU = nC(v)ΔT = 0. This is a favourite NEET trap. In free expansion of an ideal gas (into vacuum, insulated), both q = 0 and w = 0, so ΔU = 0 and ΔT = 0 too.
No. We can never find the exact absolute value of U for a system, because it contains countless types of energy at the atomic level. NCERT clearly states this. But we do not need the absolute value — for NEET and for chemistry we only ever need the CHANGE, ΔU, which we can measure using ΔU = q + w.
The correct option for free expansion of an ideal gas under adiabatic condition is:
A gas is allowed to expand in a well insulated container against a constant external pressure of 2.5 atm from an initial volume of 2.50 L to a final volume of 4.50 L. The change in internal energy ΔU of the gas in joules will be:
At a certain temperature T (K), during a process, 500 J is absorbed by the system and work of 200 J is done by the system. Then the change in internal energy of the system is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Internal energy is an extensive property — its value depends on the amount of matter in the system. Two moles of gas have twice the internal energy of one mole in the same state. NCERT lists U, along with mass, volume and enthalpy, as extensive properties.
Internal energy (U) is energy STORED inside the system and is a state function. Heat (q) is energy that FLOWS across the boundary because of a temperature difference; it is a path function. Heat can change internal energy, but heat itself is not 'stored' in the system.
Because a system stores energy in countless forms at the molecular level (bonds, motion, forces). We cannot add all of these to get one exact number. We only measure the change ΔU, which is enough for all chemistry problems.
For an ideal gas, internal energy depends ONLY on temperature. So ΔU = nC(v)ΔT. If temperature does not change (isothermal), ΔU = 0, even if heat and work are exchanged.
The first law is written as ΔU = q + w. It says the change in internal energy equals the heat added to the system plus the work done on the system. This is just the law of conservation of energy applied to a thermodynamic system.
