How Much Energy is Required to Heat 25g of Ice from -15°C to Water at 15°C

To calculate the total energy required to heat 25 grams of ice from -15°C to water at 15°C, we need to consider three distinct steps. This comprehensive guide will walk you through the calculations and provide a clear understanding of the thermal processes involved.

Thermal Processes Involved

The question presents three distinct thermal processes that need to be addressed:

Heating the ice from -15°C to 0°C Melting the ice at 0°C Heating the water from 0°C to 15°C

Step-by-Step Energy Calculation

Step 1: Heating the Ice from -15°C to 0°C

The specific heat capacity of ice is approximately 2.09 J/g°C. The formula used is:

q_1 m cdot c cdot Delta T

q_1 25 g cdot 2.09 J/g°C cdot (0 - (-15))°C
q_1 25 g cdot 2.09 J/g°C cdot 15 °C
q_1 25 cdot 2.09 cdot 15 783.75 J

Step 2: Melting the Ice at 0°C

The heat of fusion of ice is approximately 334 J/g. The formula used is:

q_2 m cdot L_f

q_2 25 g cdot 334 J/g
q_2 8350 J

Step 3: Heating the Water from 0°C to 15°C

The specific heat capacity of water is approximately 4.18 J/g°C. The formula used is:

q_3 m cdot c cdot Delta T

q_3 25 g cdot 4.18 J/g°C cdot (15 - 0)°C
q_3 25 cdot 4.18 cdot 15 1567.5 J

Calculating Total Energy Required

Now, we sum all the energies calculated for the three steps:

q_{text{total}} q_1 q_2 q_3

q_{text{total}} 783.75 J 8350 J 1567.5 J
q_{text{total}} 10701.25 J

Conclusion

The total energy required to heat 25 grams of ice from -15°C to water at 15°C is approximately 10701.25 J. This calculation demonstrates the practical application of specific heat capacity and latent heat in thermal processes.

There are three key concepts in this process:

Heat Energy: The total amount of energy needed to change the temperature or phase of a substance. Specific Heat Capacity: The amount of heat per unit mass required to raise the temperature of a substance by one degree Celsius. Latent Heat: The energy required for a substance to change its state without changing its temperature. For ice, this is the heat of fusion.