Q.No. 26 A block of ice at 0 °C is supplied heat at a constant rate to convert ice to superheated steam. Which one of the following trajectories correctly represents the trend of the temperature of the system with time? Assume that the specific heat of H₂O is not a function of temperature.
A) Temperature increases linearly with time
B) Temperature increases stepwise with plateaus
C) Temperature increases exponentially
D) Temperature remains constant

When a block of ice at 0°C receives heat at a constant rate until it becomes superheated steam, the temperature does not rise uniformly due to phase changes. The process involves heating ice to 0°C (already at start), melting to water at 0°C, heating water to 100°C, vaporizing to steam at 100°C, and then heating steam beyond 100°C. This creates distinct linear rises interrupted by plateaus where temperature stays constant during melting and boiling.

Option Analysis

A) Temperature increases linearly with time
This implies steady temperature rise without interruptions, as if no phase changes occurred. Heat would only raise temperature via specific heat, ignoring latent heats of fusion and vaporization that absorb energy without temperature change. Incorrect for real water phase transitions.

B) Temperature increases stepwise with plateaus
Correct representation: Temperature stays constant at 0°C during melting (latent heat of fusion), rises linearly from 0°C to 100°C as liquid water heats, plateaus at 100°C during boiling (latent heat of vaporization), then rises again as superheated steam. Matches constant heat rate with phase-specific energy absorption.

C) Temperature increases exponentially
Exponential rise suggests accelerating temperature gain, possibly from decreasing mass or heat capacity, but constant rate and assumed constant specific heat yield linear rises between phases. No physical basis for exponential behavior here.

D) Temperature remains constant
This ignores sensible heat additions during temperature rises (ice already at 0°C, water to 100°C, steam superheating). Constant temperature only occurs during phase changes, not the full process.

Heating Curve Explanation

At constant heat supply rate Q̇, temperature change follows:

Q̇ = mc dT/dt (single phase)

⇒ Linear T vs t when c is constant

During phase change:

Q̇ = mL dm_phase/dt

⇒ Temperature plateaus until transition completes

Energy Values

• Melting plateau at 0°C: L_f ≈ 334 kJ/kg
• Liquid heating (0–100°C): c_water ≈ 4.18 kJ/kg·K
• Boiling plateau at 100°C: L_v ≈ 2260 kJ/kg
• Steam heating (>100°C): c_steam ≈ 2.01 kJ/kg·K

The assumption of temperature-independent specific heat ensures linear segments, with plateau durations proportional to latent heats.

Correct Answer

B) Temperature increases stepwise with plateaus