Question

Specific heat of saturated water vapour at 100\(^{\circ}\)C is.

• A. zero
• B. positive
• C. negative
• D. sometimes positive, sometimes negative

Hint:

This is a famous paradox in thermodynamics. Adding heat to saturated steam can make it condense if the pressure isn't increased enough, and expanding it adiabatically causes condensation. This behavior leads to the negative specific heat capacity along the saturation curve.

Answer 1

The Correct Option is C

The specific heat of saturated water vapor is a non-intuitive concept. Saturated vapor is vapor that is in equilibrium with its liquid phase (i.e., it's on the point of condensing). Consider a process where we add heat to saturated water vapor. This added heat will tend to increase its temperature (superheat it). However, to keep the vapor in a saturated state at this new, higher temperature, the pressure must also increase significantly along the vaporization curve. To achieve this higher pressure, the vapor must be compressed. The work done on the vapor during this compression can increase its internal energy (and thus temperature) by more than the amount of heat added. In order to only reach the new saturation temperature without overshooting it, heat must actually be removed from the system. Since specific heat is defined as the heat added per unit mass per unit temperature change (\(c = \frac{dQ}{m dT}\)), and in this process \(dQ\) can be negative while \(dT\) is positive, the specific heat of saturated water vapor is negative.