An ideal gas initially in state 1 goes to a final state by one of three different processes (a, b, or c). Each of the possible final states has the same temperature.
For which process is the change in internal energy larger?
The change in temperature is the same for all three processes → the
change in internal energy is the same.
For which process is more heat transferred into the gas?
Look at the areas under the curves for each process.
Process c has the most work done by the gas or the most negative work done on the gas.
Now look at the first law of thermodynamics: dE = dQ + dW
For all three processes, dE is the same (and positive)
For process c, dW is the most negative.
Therefore for process c, dQ must be the most positive.