Specific Heat Capacity Of Water 4200, Heat Capacity Of Ice

Specific Heat Capacity Of Water 4200heat Capacity Of Ice Is 2100fusio

Calculate the amount of heat energy needed to change 2.58 kg of water at 60°C into water at 0°C, the energy required to convert water at 0°C into ice at 0°C, and the energy needed to cool ice from 0°C to -15°C. Additionally, determine whether heat flows into or out of the system during each process, providing an explanation for each case.

Paper For Above instruction

Understanding heat transfer during phase changes and temperature variations of water and ice involves applying concepts of specific heat capacity and latent heat of fusion. This study calculates the energy exchanges involved in cooling water, freezing it into ice, and further cooling the ice, offering insights into the thermodynamic direction of heat flow.

Introduction

Water’s ability to absorb or release heat during temperature changes and phase transitions is fundamental in thermodynamics. Specific heat capacity describes the amount of heat needed to raise the temperature of a substance, while latent heat accounts for the energy required for phase changes at constant temperature. In this analysis, we evaluate three sequential steps: cooling water from 60°C to 0°C, freezing water at 0°C into ice, and further cooling ice from 0°C to -15°C. The calculations illustrate how energy transfer occurs and clarify the direction of heat flow during each stage.

Calculation of heat energy to cool water from 60°C to 0°C

Given data:

  • Mass of water, m = 2.58 kg
  • Initial temperature, T₁ = 60°C
  • Final temperature, T₂ = 0°C
  • Specific heat capacity of water, c_w = 4200 J/kg°C

The heat energy required (Q₁) is calculated using the formula:

Q₁ = m × c_w × (T₁ - T₂)

Q₁ = 2.58 kg × 4200 J/kg°C × (60°C - 0°C) = 2.58 × 4200 × 60 = 649,440 J

This energy flows out of the system to cool the water, as the temperature decreases.

Calculation of heat energy to freeze water at 0°C into ice at 0°C

Given data:

  • Latent heat of fusion of water, L_f = 2100 kJ/kg = 2,100,000 J/kg

The energy required (Q₂) to convert water into ice at 0°C is:

Q₂ = m × L_f = 2.58 kg × 2,100,000 J/kg = 2.58 × 2,100,000 = 5,418,000 J

This energy is released into the surroundings during freezing, indicating heat flows out of the system.

Calculation of heat energy to cool ice from 0°C to -15°C

Given data:

  • Specific heat capacity of ice, c_i = 2100 J/kg°C
  • Temperature change, ΔT = 0°C - (-15°C) = 15°C

The heat energy (Q₃) is:

Q₃ = m × c_i × ΔT = 2.58 kg × 2100 J/kg°C × 15°C = 2.58 × 2100 × 15 = 81,270 J

Heat flows out of the system to cool the ice further, resulting in a decrease in temperature.

Summary of heat flow directions

In each stage, the direction of heat flow aligns with the thermal process: during cooling of water and ice, heat exits the system, leading to temperature reduction. During freezing, heat is released to the surroundings as the water transitions to a more energy-stable solid phase. Specifically:

  • Cooling water from 60°C to 0°C: heat flows out of the system.
  • Freezing water into ice at 0°C: heat flows out of the system.
  • Cooling ice from 0°C to -15°C: heat flows out of the system.

This clear direction of heat transfer is consistent with thermodynamic principles, where heat spontaneously moves from higher temperature regions or phases to lower temperature surroundings.

Conclusion

The calculations demonstrate the substantial energy exchange involved in cooling water, freezing it, and further lowering its temperature as ice. These processes exemplify core thermodynamic concepts such as specific heat capacity and latent heat. The overall analysis shows that in all phases of the process, heat flows out of the system, which is characteristic of processes involving cooling and phase transition from liquid to solid.

References

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