-->

Thermodynamics

Question
CBSEENCH11006154

Derive a relationship between ∆H and ∆U.

Solution
Let H1 be the enthalpy of a system in the initial state and H2 be the enthalpy of a system in the final state. Let U1 and V1 be the internal energy and volume in the initial state and let U2 and V2 be the corresponding values in the final state.
because space space space space space straight H space equals space straight U space plus space PV
therefore space space space space space straight H subscript 1 space equals space straight U subscript 1 space end subscript plus space PV subscript 1 space space space space space space space space space space... left parenthesis 1 right parenthesis
and space space space straight H subscript 2 space equals space straight U subscript 2 space plus space PV subscript 2 space space space space space space space space space space... left parenthesis 2 right parenthesis
Subtracting (1) from (2), we have,
     space straight H subscript 2 space minus straight H subscript 1 space equals space left parenthesis straight U subscript 2 plus PV subscript 2 right parenthesis space minus space left parenthesis straight U subscript 1 plus space PV subscript 1 right parenthesis
therefore space space space straight H subscript 2 space minus space straight H subscript 1 space equals space left parenthesis straight U subscript 2 space plus space PV subscript 2 right parenthesis space minus space left parenthesis straight U subscript 1 space plus space PV subscript 1 right parenthesis
therefore space space space space space increment straight H space equals space left parenthesis straight U subscript 2 space plus space PV subscript 2 right parenthesis space minus space left parenthesis straight U subscript 1 space plus space PV subscript 1 right parenthesis
therefore space space space space increment straight H space equals space increment straight U space plus space straight P increment straight V
In the above expression ∆U represents a change in internal energy and P∆V represents a change in work energy.
Thus, the change in enthalpy at constant pressure is equal to the increase in internal energy plus pressure-volume work done (work energy).