Interpretations of Partial Derivatives — Question 4

Question 4 – Solution

Strategy. Vary one physical input while fixing the other.

Step 1: Volume $P_V=-8T/V^2$, so $\boxed{P_V(4,300)=-150\ \mathrm{kPa/L}}$.

Step 2: Temperature $P_T=8/V$, so $\boxed{P_T(4,300)=2\ \mathrm{kPa/K}}$.

Step 3: Meaning Added volume lowers pressure locally; added temperature raises it. The statements are instantaneous and hold the other variable fixed.