From the ideal gas law:
\[ PV = nRT \]
Rearranging for volume:
\[ V = \left( \frac{nR}{P} \right) T \]
The slope of the line in the \( V-T \) graph for an isobaric process is proportional to \( \frac{1}{P} \). Therefore, we have:
\[ \text{Slope} \propto \frac{1}{P} \]
Comparing slopes:\[ (\text{Slope})_2 > (\text{Slope})_1 \quad \implies \quad P_2 < P_1 \]
Match List - I with List - II.
Consider the following statements:
(A) Availability is generally conserved.
(B) Availability can neither be negative nor positive.
(C) Availability is the maximum theoretical work obtainable.
(D) Availability can be destroyed in irreversibility's.
Let $ f: \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that $$ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) $$ for all $ x, y \in \mathbb{R} $. If $ f(0) = 1 $, then the value of $ 24f^{(4)}\left(\frac{5\pi}{3}\right) $ is: