Match List-I with List-II.
The relations for heat exchange and work done during thermodynamic processes are:
- (A) Isobaric: In an isobaric process (constant pressure), the heat supplied to the system is equal to the work done by the system, i.e., \( \Delta Q = \Delta W \).
- (B) Isochoric: In an isochoric process (constant volume), the change in heat is equal to the change in internal energy, i.e., \( \Delta Q = \Delta U \).
- (C) Adiabatic: In an adiabatic process (no heat exchange), \( \Delta Q = 0 \).
- (D) Isothermal: In an isothermal process (constant temperature), the change in heat is equal to the change in internal energy plus the work done by the system, i.e., \( \Delta Q = \Delta U + P \Delta V \).
Thus, the correct answer is (3).
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: