How Much Energy Is Required To Change 150.0 Grams Of Ice At -22.00°C To Water At 95.15°C?Use The Formula: Q = M ⋅ H F Q = M \cdot H_f Q = M ⋅ H F ​

Introduction

When dealing with phase changes, such as the transition from solid to liquid, it's essential to consider the energy required to facilitate this process. In the case of ice, the energy needed to change it into water is known as the latent heat of fusion (H_f). This value is a constant that depends on the substance and its temperature. In this article, we will explore the energy required to change 150.0 grams of ice at -22.00°C to water at 95.15°C using the formula: Q = m * H_f.

Understanding the Latent Heat of Fusion (H_f)

The latent heat of fusion (H_f) is the energy required to change a substance from a solid to a liquid state without a change in temperature. This value is typically expressed in units of joules per gram (J/g) or calories per gram (cal/g). For water, the latent heat of fusion is approximately 334 J/g. This means that 334 joules of energy are required to change 1 gram of ice into water at 0°C.

Calculating the Energy Required

To calculate the energy required to change 150.0 grams of ice at -22.00°C to water at 95.15°C, we can use the formula: Q = m * H_f. Here, Q represents the energy required, m is the mass of the ice (150.0 grams), and H_f is the latent heat of fusion (334 J/g).

Step 1: Convert the Temperature of the Ice

Before we can use the formula, we need to convert the temperature of the ice from Celsius to Kelvin. The formula for this conversion is: T(K) = T(°C) + 273.15. Plugging in the value, we get: T(K) = -22.00°C + 273.15 = 251.15 K.

Step 2: Calculate the Energy Required

Now that we have the temperature of the ice in Kelvin, we can use the formula: Q = m * H_f. Plugging in the values, we get: Q = 150.0 g * 334 J/g = 50100 J.

Step 3: Consider the Energy Required to Raise the Temperature of the Water

In addition to the energy required to change the ice into water, we also need to consider the energy required to raise the temperature of the water from 0°C to 95.15°C. This energy can be calculated using the formula: Q = m * c * ΔT, where c is the specific heat capacity of water (approximately 4.184 J/g°C) and ΔT is the change in temperature (95.15°C - 0°C = 95.15°C).

Step 4: Calculate the Energy Required to Raise the Temperature of the Water

Plugging in the values, we get: Q = 150.0 g * 4.184 J/g°C * 95.15°C = 79451.4 J.

Step 5: Calculate the Total Energy Required

To find the total energy required, we need to add the energy required to change the ice into water and the energy required to raise the temperature of the water. This gives us: Q_total = 50100 J + 79451.4 J = 129551.4 J.

Conclusion

In conclusion, the energy required to change 150.0 grams of ice at -22.00°C to water at 95.15°C is approximately 129551.4 joules. This value includes the energy required to change the ice into water and the energy required to raise the temperature of the water from 0°C to 95.15°C.

References

• Latent heat of fusion (H_f) for water: 334 J/g
• Specific heat capacity of water (c): 4.184 J/g°C
• Temperature of the ice: -22.00°C
• Temperature of the water: 95.15°C
• Mass of the ice: 150.0 grams

Calculations

Note: The calculations are based on the given values and formulas. The results are approximate and may vary depending on the specific conditions and assumptions.

Introduction

In our previous article, we explored the energy required to change 150.0 grams of ice at -22.00°C to water at 95.15°C. We used the formula: Q = m * H_f to calculate the energy required to change the ice into water and the formula: Q = m * c * ΔT to calculate the energy required to raise the temperature of the water. In this article, we will answer some frequently asked questions related to this topic.

Q: What is the latent heat of fusion (H_f) for water?

A: The latent heat of fusion (H_f) for water is approximately 334 J/g. This means that 334 joules of energy are required to change 1 gram of ice into water at 0°C.

Q: What is the specific heat capacity of water (c)?

A: The specific heat capacity of water (c) is approximately 4.184 J/g°C. This means that 4.184 joules of energy are required to raise the temperature of 1 gram of water by 1°C.

Q: How much energy is required to change 100 grams of ice at -10.00°C to water at 80.00°C?

A: To calculate the energy required, we need to use the formula: Q = m * H_f to change the ice into water and the formula: Q = m * c * ΔT to raise the temperature of the water. Plugging in the values, we get: Q = 100 g * 334 J/g = 33400 J (to change the ice into water) and Q = 100 g * 4.184 J/g°C * 90.00°C = 376760 J (to raise the temperature of the water). The total energy required is: Q_total = 33400 J + 376760 J = 410160 J.

Q: How much energy is required to change 200 grams of ice at -20.00°C to water at 90.00°C?

A: To calculate the energy required, we need to use the formula: Q = m * H_f to change the ice into water and the formula: Q = m * c * ΔT to raise the temperature of the water. Plugging in the values, we get: Q = 200 g * 334 J/g = 66800 J (to change the ice into water) and Q = 200 g * 4.184 J/g°C * 90.00°C = 751680 J (to raise the temperature of the water). The total energy required is: Q_total = 66800 J + 751680 J = 818680 J.

Q: What is the energy required to change 1 kilogram of ice at -10.00°C to water at 80.00°C?

A: To calculate the energy required, we need to use the formula: Q = m * H_f to change the ice into water and the formula: Q = m * c * ΔT to raise the temperature of the water. Plugging in the values, we get: Q = 1000 g * 334 J/g = 334000 J (to change the ice into water) and Q = 1000 g * 4.184 J/g°C * 90.00°C = 3767600 J (to raise the temperature of the water). The total energy required is: Q_total = 334000 J + 3767600 J = 4101600 J.

Q: What is the energy required to change 500 grams of ice at -15.00°C to water at 85.00°C?

A: To calculate the energy required, we need to use the formula: Q = m * H_f to change the ice into water and the formula: Q = m * c * ΔT to raise the temperature of the water. Plugging in the values, we get: Q = 500 g * 334 J/g = 167000 J (to change the ice into water) and Q = 500 g * 4.184 J/g°C * 85.00°C = 1782200 J (to raise the temperature of the water). The total energy required is: Q_total = 167000 J + 1782200 J = 1948200 J.

Conclusion

In conclusion, the energy required to change ice to water depends on the mass of the ice, the initial temperature of the ice, and the final temperature of the water. We can use the formula: Q = m * H_f to calculate the energy required to change the ice into water and the formula: Q = m * c * ΔT to calculate the energy required to raise the temperature of the water. By plugging in the values, we can calculate the total energy required to change ice to water.

References

• Latent heat of fusion (H_f) for water: 334 J/g
• Specific heat capacity of water (c): 4.184 J/g°C
• Temperature of the ice: -10.00°C, -20.00°C, -15.00°C
• Temperature of the water: 80.00°C, 90.00°C, 85.00°C
• Mass of the ice: 100 grams, 200 grams, 500 grams, 1 kilogram

Calculations

Note: The calculations are based on the given values and formulas. The results are approximate and may vary depending on the specific conditions and assumptions.