Rigid vessel, saturated steam cooling:\nOne kilogram of saturated steam at 100°C and 1.01325 bar is held in a rigid vessel of volume 1.673 m^3 and cooled to 98°C (saturation pressure 0.943 bar). At 98°C, one kilogram of saturated water vapor occupies 1.789 m^3. Estimate the latent heat of condensation (kJ/kg) under these conditions.

Introduction / Context:
Steam in a rigid, closed vessel undergoes condensation when cooled at saturation. Because the container volume is fixed, part of the vapor condenses to meet the new saturation specific volume at the lower temperature. This classic thermodynamics exercise links mass–volume balance with latent heat magnitudes near 100°C.

Given Data / Assumptions:

• Initial state: saturated vapor, T1 = 100°C, V_total = 1.673 m^3, m_total = 1 kg.
• Final state: saturated mixture at T2 = 98°C, p2 = 0.943 bar.
• Specific volume of saturated vapor at 98°C: v_g2 = 1.789 m^3/kg.
• Neglect vessel heat capacity and kinetic/potential energy effects.

Concept / Approach:
At the final saturated state, some vapor remains and the rest is condensate (liquid) occupying negligible volume compared with vapor near 100°C. Use the rigid-volume constraint to find vapor mass, then the condensed mass. The latent heat value near 100°C is about 2257–2260 kJ/kg; the problem tests consistency with typical steam-table values.

Step-by-Step Solution:
Let m_v be mass of vapor at 98°C. The vapor occupies nearly all the volume: m_v * v_g2 ≈ V_total.Compute m_v = 1.673 / 1.789 ≈ 0.936 kg.Condensed mass m_c = 1 − 0.936 ≈ 0.064 kg.Latent heat at ~100°C is close to 2260 kJ/kg; choices include 2263 kJ/kg, which matches standard values.

Verification / Alternative check:
Steam tables near 100°C give h_g − h_f ≈ 2256–2260 kJ/kg; at 98°C, the value is within a few kJ/kg of 2260. Hence 2263 kJ/kg is the appropriate selection.

Why Other Options Are Wrong:
2676 kJ/kg: corresponds more to latent heat at lower pressures/high superheat contexts; not near 100°C saturation.40732 and 540 kJ/kg: orders of magnitude or phase-change type are incorrect; 540 is closer to water’s specific heat per kg raising 1 kJ/kg·K over 540 K, which is irrelevant here.

Common Pitfalls:
Forgetting the rigid-volume constraint; assigning significant volume to the small liquid fraction; mixing specific volume data across temperatures.

Final Answer:
2263