# Does the Internal Energy remain constant during Isothermal Process carrying Heat/Work interactions?

- Scenario-1:

Work is done on an insulated system then Change in Internal Energy will be..

del(E) = - W

- Scenario-2:

Work is done on the same system(diathermic in this case) but transferring some amount of heat to its surrounding then, What will be the change in Internal Energy ?

• conductive, non-insulated, Heat Interactive, etc. – Zaid AAmir Aug 2 '17 at 7:01

We use the First Law of Thermodynamics,

$$dU=dQ+W.$$

In scenario 1, $dQ=0$ since the system is insulated, so $dU=W$, where $W$ is defined as the work done on the system and $dU$ is the corresponding change in internal energy.

In scenario 2, the system allows the passage of some heat, so $dQ$ is allowed to be nonzero (but still could be zero, i.e. for an adiabatic process). Here's where things get complicated. We can't actually say anything about the sign or magnitude of $dQ$ in general, since that depends on the particular way that work is done on the system (for an ideal gas, this refers to the particular path of the process in $PV$-space). As such, we cannot determine the value or sign of $dU$ in general.

However, if the system is an ideal gas or incompressible solid, and if we know the system's temperature is constant, then, since internal energy is proportional to temperature, $dU=0$ in this case.

• if the temperature remained constant (Isothermal) in both scenario, will the energy change be constant ? – Zaid AAmir Aug 2 '17 at 7:14
• Internal energy is a function of temperature only, so $dU=0$ in that case. – probably_someone Aug 2 '17 at 7:18
• So, if this comment is appended to the above scenario, will dU = 0 ? – Zaid AAmir Aug 2 '17 at 7:23
• @ZaidAAmir See edited answer. – probably_someone Aug 2 '17 at 7:32
• @ChesterMiller I know, which is why I edited my answer to reflect that. – probably_someone Aug 3 '17 at 19:30