Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
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.
Options:
(A) Time
(B) Temperature
Time
(C) Temperature
Time
(D) Temperature
Time
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2020 Q.36)**
**1. Governing Concept**:
- **Topic**: Thermodynamics & Phase Change Calorimetry
- When heat is supplied at a constant rate $Q$ to a block of ice initially at $0^\circ\text{C}$:
1. **Phase 1 (Latent heat of fusion)**: Ice melts into liquid water at a constant temperature of $0^\circ\text{C}$ ($T$ remains flat at $0^\circ\text{C}$ while heat is absorbed: $Q = m L_f$).
2. **Phase 2 (Sensible heating of water)**: Once all ice has melted into water, temperature rises linearly with time: $\frac{dT}{dt} = \frac{\dot{Q}}{m c_w}$.
3. **Phase 3 (Latent heat of vaporization)**: At $100^\circ\text{C}$, water boils and temperature plateaus at $100^\circ\text{C}$ ($Q = m L_v$).
- Curve (A) represents this exact thermal profile: an initial flat plateau at $0^\circ\text{C}$, followed by linear temperature increase, followed by a flat plateau at $100^\circ\text{C}$.
**2. Option Analysis**:
- **Option (A) is CORRECT**: Accurately depicts isothermal fusion plateau at $0^\circ\text{C}$, sensible warming, and isothermal vaporization plateau at $100^\circ\text{C}$.
- **Option (B) is INCORRECT**: Shows temperature rising immediately without fusion plateau.
- **Option (C) is INCORRECT**: Omits boiling plateau.
- **Option (D) is INCORRECT**: Parabolic non-thermodynamic curve.
**3. Final Answer**:
- **Correct Choice**: **A**
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