# What is the difference between work done and energy transfer

I understand that work done is a form of energy transfer, but I am I right in thinking that energy can be transferred without work being done?

If so, what is it that makes the two different. In particular, in the case of thermodynamics, what is the difference between simply transferring energy to a gas (such as heating) and actually doing work on the gas.

Thanks.

• "Work" simply means the transfer of energy. That is why systems with reversible processes have infinite capacity for work - but then we say, it does no useful work. Jan 26, 2018 at 0:09

In thermodynamics, work is the negative of the change in internal energy due to a change in volume, usually holding entropy and particle numbers constant. This takes the form of a force pushing on the walls of the volume, which connects it to our conventional notion of work, $W = F~\Delta x$, as seen for example if we consider a cylinder of cross-section $A$, $$W = F~\Delta x = F~\frac AA~\Delta x = \frac FA~A\Delta x = P ~\Delta V.$$And the change in internal energy is just the negative of the work, $-P~\Delta V,$ due to the law of energy conservation.

In fact we can also define that $W = P~\Delta V$ even when we are not holding entropy and particle numbers constant: but then it is not necessarily the same as the change in internal energy. So for example if you compress an ideal gas it generally heats up; you could still speak of the work as $P~\Delta V$ at constant temperature, but "at constant temperature" means essentially "we squeeze this thing and it wants to become warmer, but we let energy out of the system through the walls until it comes back to the same temperature": there has been a negative work, and perhaps the internal energy has still gone up, but it has not gone up as much as it would have had the walls been thermodynamic insulators. In these cases however we can often define a "free energy" (in this case $E - T S$) which the work is the negative of the change of.

As @Steve has commented: work means the transfer of energy.

In thermodynamics, the internal energy of a gas changes in response to work done between any defined initial and final states, according to the equation $\Delta U=\sum_{i} E_i$ where $\Delta U$ is the change in internal energy of the gas and $E_i$ are the various energies transferred to the gas between the initial and final states. Examples of work done are:

• Heating the gas. This is by definition positive work on the gas. If the gas is in a closed system, then its volume cannot increase, then The heat added will be measurable as increases in the temperature and pressure of the gas.
• Cooling the gas. Negative work on the gas. For a fixed volume closed gas, temperature and pressure drop.
• Compressing the gas. Positive work on the gas. If the gas is in a closed container, the pressure will rise, and so will temperature, if no other work is done.

A very useful example of work being done on a gas to transfer energy is air conditioning (also see refrigeration cycle schematic below). Air conditioners with a compression cycle carry a fluid called a refrigerant, in a pipe, and work as follows to cool a room:

1. Inside the room, a compressed refrigerant liquid is passed through a valve. As it passes through the valve, its pressure drops enough to turn it into a gas. The refrigerant in gas form is significantly colder than in its liquid form.
2. The cold gas absorbs heat from the room, increasing the temperature, and thus the internal energy of the gas.
3. As the fluid flows in the pipe to the outside of the room, it is sent to a 'condenser'. There, it is compressed, turning it into a liquid again.
4. The refrigerant in its liquid state is significantly hotter than in its gas state, so it loses heat to the outside air.
5. The cycle repeats.