Write down the mathematical form of the first law of thermodynamics for an infinitesimal change that involves only pressure-volume work. Write down the form of this equation if the above change occurs reversibly.

Explanation

In case of an infinitesimal change, the mathematical form of the first law of thermodynamics is : `dU=deltaq+deltaw`, where `deltaq`=heat abosrobed by the system, `deltaw=`work done on the the system and dU is the change in internal energy of the system.
For an infinitesimal change involving only P-V work, `deltaw=-P_(ex)dV`. so, for an infinitesimal change involving only P-V work, the form of the first law of thermodynamics will be, `dU=deltaq-P_(ex)dV`
In case of a reversible process, `P_(ex)=P` (pressure of the system). so, `dU=deltaq-PdV`.