Latent heat of vaporisation: Identify the correct overall trend with temperature and pressure, and its value at the critical point.

Introduction / Context:
Latent heat of vaporisation is the energy required to convert saturated liquid to saturated vapour at a given pressure/temperature. Its variation with T and P is foundational in boiler design, refrigeration, and power cycles.

Given Data / Assumptions:

• Considering a pure component undergoing liquid–vapour phase change.
• Equilibrium transitions along the saturation curve up to the critical point.

Concept / Approach:
As temperature increases toward the critical temperature, the enthalpy difference between saturated liquid and vapour shrinks because liquid and vapour properties converge. Similarly, at higher pressures along the saturation curve, the two phases become more alike. At the critical point, the phases are indistinguishable, so latent heat is zero.

Step-by-Step Solution:

Verification / Alternative check:
Steam tables show h_g − h_f decreasing as T approaches the critical temperature (for water, near 374 °C), confirming the trend.

Why Other Options Are Wrong:

• Each individual statement (a), (b), (c) is correct; therefore the combined choice “all (a), (b) & (c)” is appropriate.

Common Pitfalls:
Assuming latent heat is constant or increases with temperature; in reality it declines to zero at the critical point.

Final Answer:
all (a), (b) & (c)