The first Law of Thermodynamics

The first law of thermodynamics states that energy can neither be created nor destroyed, although it can be transformed from one form to another. This is also known as the law of conservation of energy. 

Mathematical Expression of First Law

Let U_A be the energy of a system in its state A and U_B be the energy in its state B. Suppose the system while undergoing change from state A to state B absorbs heat q from the surroundings and also performs some work (mechanical or electrical), equal to w. The absorption of heat by the system tends to raise the energy of the system. The performance of work by the system, on the other hand, tends to lower the energy of the system because performance of work requires expenditure of energy. Hence the change of internal energy, ΔU, accompanying the above process will be given by

     ΔU = U_B – U_A = q – w 

In general, if in a given process the quantity of heat transferred from the surrounding to the system is q and work done in the process is w, then the change in internal energy,

     ΔU = q + w

This is the mathematical statement of the first law of thermodynamics.

If work is done by the surroundings on the system (as during the compression of a gas), w is taken as positive so that ΔU = q + w. if however work is done by the system on the surroundings (as during the expansion of a gas), w is taken as negative so that ΔU = q – w.

Solved Example: 1 mole of ideal monoatomic gas at 27°C expands adiabatically against a constant external pressure of 1.5 atm from a volume of 4dm³ to 16 dm^3. 

Calculate (i) q (ii) w and (iii) ΔU 

Solution: (i)  Since process is adiabatic  q = 0

             (ii) As the gas expands against the constant external pressure.

                  W = –PΔV = –1.6(V₂–V₁)

                      = –1.5 (16–4) = –18 atm dm³

             (iii) ΔU = q + w = 0 + (–18) = –18 atm dm³ 

Exercise: 

Calculate the internal energy change, when a system absorbs 5 KJ of heat and does 1 KJ of work.