Math Problem Statement

A bucket of ice at 0°C starts to melt when it was placed in a warm room. During the phase change from solid to gas, it absorbs 7.30×10⁶ J of energy. What is the change in entropy of the ice?

Solution

To calculate the change in entropy (ΔS) during the melting of the ice, we use the formula:

ΔS=QT\Delta S = \frac{Q}{T}

Where:

  • QQ is the heat energy absorbed (7.30 × 10⁶ J),
  • TT is the temperature in Kelvin. Since the ice starts at 0°C, which is 273.15 K.

Now, plugging in the values:

ΔS=7.30×106J273.15K\Delta S = \frac{7.30 \times 10^6 \, \text{J}}{273.15 \, \text{K}}

Let me calculate this for you. Given values Q = 7.30e6 # Heat energy absorbed in joules T = 273.15 # Temperature in Kelvin

Calculate change in entropy

delta_S = Q / T delta_SThe change in entropy (ΔS\Delta S) of the ice is approximately 26,725 J/K.

If you need more details or have any further questions, feel free to ask! Here are some related questions to explore:

  1. How does the phase change from solid to liquid affect the entropy?
  2. What would happen to the entropy if the ice started at a different temperature?
  3. How is entropy related to the heat energy absorbed during phase transitions?
  4. What are some other factors that influence the change in entropy?
  5. How does the change in entropy differ in a reversible process compared to an irreversible one?

Tip: Always remember that entropy increases when energy is added to a system, especially during phase transitions like melting or vaporization.

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Math Problem Analysis

Mathematical Concepts

Thermodynamics
Entropy
Phase Change

Formulas

ΔS = Q / T

Theorems

Second Law of Thermodynamics

Suitable Grade Level

Undergraduate Physics