Question

. Give various forms in which first law of thermodynamics can be stated. Also explain its mathematical form.

Answer 1

An example of a physical statement is that of Planck (1897/1903):

"It is in no way possible, either by mechanical, thermal, chemical, or other devices, to obtain perpetual motion, i.e. it is impossible to construct an engine which will work in a cycle and produce continuous work, or kinetic energy, from nothing."

This physical statement is restricted neither to closed systems nor to systems with states that are strictly defined only for thermodynamic equilibrium; it has meaning also for open systems and for systems with states that are not in thermodynamic equilibrium.

An example of a mathematical statement is that of Crawford (1963):

For a given system we let ΔE (kinetic) = large-scale mechanical energy,
 ΔE (potential) = large-scale potential energy, and 
ΔE (total) = total energy.
The first two quantities are specifiable in terms of appropriate mechanical variables, and by definition:-
E(total)= E(kinetic)+ E(potential)+U
For any finite process, whether reversible or irreversible
ΔE(total)=ΔE(kinetic)+ ΔE(potential)+ ΔU
The first law in a form that involve principle of conservation of energy more generally is
ΔE(total)=Q+W
Here Q and W are heat and work added, with no restrictions as to whether the process is reversible,Here Q and W are heat and work added, with no restrictions as to whether the process is reversible, quasi static, or , irreversible
This statement by Crawford, for W, uses the sign convention of IUPAC, not that of Clausius. Though it does not explicitly say so, this statement refers to closed systems, and to internal energy U defined for bodies in states of thermodynamic equilibrium, which possess well-defined temperatures