Heat Requirements for Phase Changes: Converting Ice at -10°C to Steam at 100°C

Introduction to the Problem

When considering the transformation of 20 grams of ice from -10°C to steam at 100°C, different amounts of heat are required depending on the phase changes involved. This process involves four distinct steps:

Heating the ice from -10°C to 0°C. Melting the ice at 0°C. Heating the resulting water from 0°C to 100°C. Vaporizing the water at 100°C.

Understanding and calculating these heat requirements is crucial for a comprehensive grasp of thermodynamics and heat transfer principles.

Concept of Heat Requirements

Although I cannot perform the complete calculations for you, I can guide you through the process. Each phase change requires a specific amount of energy, known as the latent heat, which differs based on the substances and temperature changes involved. The specific heat capacity and latent heat values are key parameters in solving such problems.

Calculations for 12g of Ice at -10°C to 100°C Steam

Let's illustrate the process with 12 grams of ice transformed from -10°C to 100°C steam.

Heating Ice: Use the specific heat of ice to calculate the energy required to raise the temperature of the ice. Melting Ice: Use the latent heat of fusion to calculate the energy needed to melt the ice at 0°C. Heating Water: Use the specific heat of water to calculate the energy required to raise the temperature of the resulting water from 0°C to 100°C. Vaporizing Water: Use the latent heat of vaporization to calculate the energy required to convert the water into steam at 100°C.

For practical purposes, you can use the following values:

Specific heat of ice: 2.09 J/g·°C Latent heat of fusion (ice to liquid): 334 J/g Specific heat of water: 4.18 J/g·°C Latent heat of vaporization (liquid to steam): 2260 J/g

Step-by-Step Calculations

Now let's solve the problem step-by-step for 12 grams of ice at -10°C to 100°C steam:

1. Heating the Ice from -10°C to 0°C

The formula to calculate the energy required is:

q1 mcΔT

Where:

q1 energy required (J)

m mass of ice (g)

c specific heat capacity of ice (J/g·°C)

ΔT temperature change (°C)

Substituting the values:

q1 12g × 2.09 J/g·°C × 10°C 250.8 J

2. Melting the Ice at 0°C

The formula to calculate the energy required is:

q2 m × latent heat of fusion

Substituting the values:

q2 12g × 334 J/g 4008 J

3. Heating the Water from 0°C to 100°C

The formula to calculate the energy required is:

q3 mcΔT

Where:

q3 12g × 4.18 J/g·°C × 100°C 5040 J

4. Vaporizing the Water at 100°C

The formula to calculate the energy required is:

q4 m × latent heat of vaporization

Substituting the values:

q4 12g × 2260 J/g 27120 J

Adding Up the Energies

The total energy required is the sum of the energies from steps 1 to 4:

Total energy (q) q1 q2 q3 q4

q 250.8 J 4008 J 5040 J 27120 J

Total energy 36418.8 J or 36.4188 kJ

For significant figures, the answer can be rounded to:

36000 J or 36 kJ

Conclusion

By understanding and applying the principles of heat transfer and phase changes, you can effectively calculate the heat requirements for converting 20 grams of ice from -10°C to steam at 100°C. This process involves a series of carefully calculated steps, each crucial for a complete transformation.

Feel free to practice these calculations with different mass values and temperatures to enhance your understanding of thermodynamic concepts. Proper application of these principles is not only educational but also useful in practical applications such as heating and cooling systems, refrigeration, and industrial processes.