Worksheet on specific latent heat involving melting ice and energy calculations.

Here are the step-by-step solutions for the problems shown on the worksheet.

Part 1: Melting Ice

*Formulas used:*
* Heating water/ice: $Q = m \cdot c \cdot \Delta T$
* Melting ice (phase change): $Q = m \cdot L_f$
* Values given: $c_{water} = 4186$, $L_f = 334,000$

1. How much energy is needed to melt 5 kg of ice at 0°C?
* Since the ice is already at 0°C, we only need the energy to change it from solid to liquid (melting).
* Calculation: $5 \text{ kg} \times 334,000 \text{ J/kg}$
* Result: $1,670,000 \text{ J}$

2. How much energy is needed to raise 2.5 kg of water at 0°C to 100°C?
* This is just heating the water, no phase change yet.
* Change in temperature ($\Delta T$) = $100 - 0 = 100^\circ\text{C}$.
* Calculation: $2.5 \text{ kg} \times 4186 \text{ J/kg}^\circ\text{C} \times 100^\circ\text{C}$
* Result: $1,046,500 \text{ J}$

3. How much energy is needed to vaporize 50 g of water at 100°C?
* First, convert grams to kilograms: $50 \text{ g} = 0.05 \text{ kg}$.
* Use the Latent Heat of Vaporization ($L_v = 2,260,000$).
* Calculation: $0.05 \text{ kg} \times 2,260,000 \text{ J/kg}$
* Result: $113,000 \text{ J}$

4. How much energy is needed to vaporize 30 g of water at 100°C?
* Convert grams to kilograms: $30 \text{ g} = 0.03 \text{ kg}$.
* Calculation: $0.03 \text{ kg} \times 2,260,000 \text{ J/kg}$
* Result: $67,800 \text{ J}$

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Part 2: Turn up the heat!

*New Value given:* Specific Heat of Steam ($c_{steam}$) = $2108.5 \text{ J/kg}^\circ\text{C}$

5. How much energy is needed to raise 5 kg of steam at -210.5°C to 100°C?
*(Note: The starting temperature in the image appears to be a typo and likely should be positive, e.g., 10.5°C or similar, because standard steam doesn't exist at negative temperatures. However, I will solve it exactly as written using the numbers provided).*
* Change in temperature ($\Delta T$) = Final Temp - Initial Temp = $100 - (-210.5) = 310.5^\circ\text{C}$.
* Calculation: $5 \text{ kg} \times 2108.5 \text{ J/kg}^\circ\text{C} \times 310.5^\circ\text{C}$
* Result: $3,273,971.25 \text{ J}$

6. How much energy is needed to vaporize 5 kg of water at 100°C?
* Use Latent Heat of Vaporization ($L_v = 2,260,000$).
* Calculation: $5 \text{ kg} \times 2,260,000 \text{ J/kg}$
* Result: $11,300,000 \text{ J}$

7. How much energy is needed to vaporize 100 g of water at 22.5°C?
This problem has two steps:
* Step A: Heat the water from 22.5°C to 100°C.
* $\Delta T = 100 - 22.5 = 77.5^\circ\text{C}$.
* Mass = $0.1 \text{ kg}$.
* Energy = $0.1 \times 4186 \times 77.5 = 32,441.5 \text{ J}$.
* Step B: Vaporize the water at 100°C.
* Energy = $0.1 \times 2,260,000 = 226,000 \text{ J}$.
* Total: $32,441.5 + 226,000$
* Result: $258,441.5 \text{ J}$

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Part 3: Was this a fail?

8. How much energy is needed to melt 50 kg of carbon dioxide at -114°C?
* Use Latent Heat of Fusion for CO2 ($L_f = 1.8 \times 10^5 = 180,000$).
* Calculation: $50 \text{ kg} \times 180,000 \text{ J/kg}$
* Result: $9,000,000 \text{ J}$

9. How much energy is needed to vaporize 300 g of carbon dioxide at -22°C?
* Convert mass to kg: $300 \text{ g} = 0.3 \text{ kg}$.
* Use Latent Heat of Vaporization for CO2 ($L_v = 5.7 \times 10^5 = 570,000$).
* Calculation: $0.3 \text{ kg} \times 570,000 \text{ J/kg}$
* Result: $171,000 \text{ J}$

Final Answer:
1. 1,670,000 J
2. 1,046,500 J
3. 113,000 J
4. 67,800 J
5. 3,273,971.25 J
6. 11,300,000 J
7. 258,441.5 J
8. 9,000,000 J
9. 171,000 J