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First Law of Thermodynamics

Having the knowledge of internal energy, heat and work, we will move little bit further to define a law, which is called as first law of thermodynamics.

The first law of thermodynamics connects heat, work and internal energy.

"Whenever heat is supplied to a body, a part of it is used to increase its internal energy i.e., to raise its temperature and the rest in doing external work"

If is the heat energy absorbed by a system, the increase in its internal energy and the external work done by it, then provided all the quantities are measured in units of work,
  • ∆Q = Heat supplied to the system by the surroundings
  • ∆W = Work done by the system on the surroundings
  • ∆U = Change in internal energy
According to the general principle of conservation of energy, the above equations can be written as,
The above equation is a mathematical form of first law of thermodynamics.
The first law of thermodynamics establishes the essential equivalence between the work and heat, as according to this law, the internal energy and hence temperature of a system can be increased either by supplying heat to it or by doing work on the system or both.
Sign Convention
  • When heat is supplied to a system, ∆Q is taken as positive. When heat is drawn from the system, ∆Q is taken as negative.
  • When a gas expands, work done by the gas, ∆W is taken as positive. When a gas is compressed work is done on the gas, ∆W is taken as negative.
  • When temperature of a gas increases, its internal energy increases, ∆U is taken as positive. When temperature of a gas decreases, its internal energy decreases, ∆U is taken as negative.

Suppose a system changes from a state characterized by (P1, V1) to a state characterized by (P2, V2).

This can be achieved by changing the volume V1 to V2 keeping the pressure as constant. Then changing the pressure P1 to P2 keeping the volume as constant
So that the system reaches to a final state (P2, V2).

The final state (P2, V2) can be achieved alternatively by keeping volume constant at first and then keeping the pressure constant.

Since U is state variable, depends only on the initial and final states not on the path taken by the gas.

∆Q = Point Variable or State Variable
∆W and ∆U are Path Variable

∆Q - ∆W is also path independent which means it is also a state variable.

Suppose a system is taken from one state to another state through a process such that ∆U = 0, then we can say that

∆Q = ∆U + ∆W ∆Q = 0+∆W ∆Q = ∆W

This equation implies that the total amount of heat energy supplied to the system is entirely used up by the system in doing work on the surroundings.

If the system is in a cylinder with a movable piston, then the system does work when moving the piston. Then the work done can be expressed as


∆Q =∆U + P ∆V

Limitations of the First Law of Thermodynamics:

  1. The first law does not indicate the direction in which the change can occur.
  2. The first law does not give any idea about the extent of change i.e. Heat energy to Mechanical energy or Mechanical energy to Heat energy.
  3. The first law of thermodynamics gives no information about the source of heat i.e. whether it is a hot or a cold body.

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