Question

can work be done by a system without changing its volume ?Explain your answer .

Answer 1

It depends on how you define work. Work is sometimes defined as pressure times a change in volume (pΔVpΔV, or ∫pdV∫pdV if the pressure is not constant), which is equivalent to force times distance, as John Rennie defines it in his answer. In this case it's necessary for the volume to change, purely from the definition.

However, another way to define work is something along the lines of "a change in energy that is not due to the transfer of heat or thermal radiation." In this case it is not necessary for the volume to change. A particular example where the word "work" is used in this way is in electronics, when one calculates the work involved in charging a capacitor as ∫VdQ∫VdQ, where VV here is the voltage rather than the volume, and Q is the charge. In this case neither the volume of the capacitor nor the battery charging it changes, but work is said to be done because the internal energy of the capacitor has changed reversibly, without a transfer of heat.

To put it more mathematically, consider the fundamental equation of thermodynamics:

dU=TdS−pdV+∑iμidNi+…dU=TdS−pdV+∑iμidNi+…(where the "……" can include many other optional terms, including a VdQVdQ one for a capacitor). The right-hand side of this equation represents all the ways in which a system's energy can change. The first term (TdSTdS) represents a transfer of heat. Some people define "work" as just the second term (−pdV−pdV), whereas others define it as the sum of all the other terms apart from the first one. Thus, with the second definition you can have work that's associated with a change in volume, but you can also have work that's associated with a change in the chemical composition, charge, or any other conserved quantity.