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THERMODYNAMICS 139 the route taken. Volume of water in a pond, for One way: We do some mechanical work, say example, is a state function, because change 1 kJ, by rotating a set of small paddles and thereby churning water. Let the new state in volume of its water is independent of the be called B state and its temperature, as route by which water is filled in the pond, T . It is found that T > T and the change either by rain or by tubewell or by both. B B A in temperature, ∆T = T B–TA. Let the internal (b) Heat energy of the system in state B be U Band the change in internal energy, ∆U =U B– UA. We can also change the internal energy of a system by transfer of heat from the Second way: We now do an equal amount surroundings to the system or vice-versa (i.e., 1kJ) electrical work with the help of an immersionrod andnotedownthetemperature without expenditure of work. This exchange change. We find that the change in temperature of energy, which is a result of temperature difference is called heat, q. Let us consider is same as in the earlier case, say, B– TA. bringingaboutthesamechangeintemperature In fact, the experiments in the above (the same initial and final states as before manner were done by J. P. Joule between in section 5.1.4 (a) by transfer of heat 1840–50 and he was able to show that a through thermally conducting walls instead given amount of work done on the system, no matter how it was done (irrespective of of adiabatic walls (Fig. 5.4). path) produced the same change of state, as measured by the change in the temperature of the system. So, it seems appropriate to define a quantity, the internal energy U, whose value is characteristic of the state of a system, whereby the adiabatic work, w required to bring about a change of state is equal to the difference between the value of U in one state and that in another state, ∆U i.e., ∆U =U 2–U 1 w ad Fig. 5.4 A system which allows heat transfer Therefore, internal energy, U, of the system is a state function. through its boundary. By conventions of IUPAC in chemical We take water at temperature, T A in a thermodynamics. The positive sign expresses container having thermally conducting walls, that w is positive when work is done on the say made up of copper and enclose it in a ad huge heat reservoir at temperature, T . The system and the internal energy of system heat absorbed by the system (water), q can be increases. Similarly, if the work is done by the system, w adwill be negative because internal measured in terms of temperature difference, energy of the system decreases. T B– TA. In this case change in internal energy, ∆U = q, when no work is done at constant Can you name some other familiar state volume. functions? Some of other familiar state functions are V, p, and T. For example, if we By conventions of IUPAC in chemical thermodynamics. The q is positive, when heat bring a change in temperature of the system is transferred from the surroundings to the from 25°C to 35°C, the change in temperature is 35°C–25°C = +10°C, whether we go straight system and the internal energy of the system up to 35°C or we cool the system for a few increases and q is negative when heat is degrees, then take the system to the final transferred from system to the surroundings resulting in decrease of the internal energy of temperature. Thus, T is a state function and the change in temperature is independent of the system. * Earlier negative sign was assigned when the work is done on the system and positive sign when the work is done by the system. This is still followed in physics books, although IUPAC has recommended the use of new sign convention. Reprint 2026-27