Question:medium

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

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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.
Updated On: Feb 10, 2026
  • zero
  • positive
  • negative
  • sometimes positive, sometimes negative
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The Correct Option is C

Solution and Explanation

The specific heat of saturated water vapor is counter-intuitive. Saturated vapor exists in equilibrium with its liquid phase, meaning it is on the verge of condensation. When heat is added to saturated water vapor, it attempts to increase the vapor's temperature (superheating). However, to maintain the saturated state at an elevated temperature, the pressure must also rise substantially along the vaporization curve, necessitating compression of the vapor. The work performed on the vapor during compression can increase its internal energy and temperature by an amount exceeding the heat input. Consequently, to achieve the new saturation temperature without exceeding it, heat must be extracted from the system. Given that specific heat is defined as the heat added per unit mass per unit temperature change (\(c = \frac{dQ}{m dT}\)), and in this scenario, \(dQ\) can be negative while \(dT\) is positive, the specific heat of saturated water vapor is negative.
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