How much heat must be added to 60 g of water at an initial temperature of 22°C to

a. Heat it to the boiling point?

b. Completely convert the 100°C water to steam?

To solve this, we need to use the concepts of specific heat and latent heat.

### Part a: Heating water to the boiling point
We’ll use the formula for heat transfer:
\[
Q = mc\Delta T
\]
Where:
- \( Q \) is the heat energy in joules (J),
- \( m \) is the mass of the water (60 g = 0.060 kg),
- \( c \) is the specific heat capacity of water (\( c = 4.18 \, \text{J/g°C} \) or \( 4180 \, \text{J/kg°C} \)),
- \( \Delta T \) is the change in temperature.

The initial temperature is 22°C, and the boiling point of water is 100°C, so:
\[
\Delta T = 100°C - 22°C = 78°C
\]

Now, we can calculate the heat needed:
\[
Q = (0.060 \, \text{kg})(4180 \, \text{J/kg°C})(78°C) = 19,548 \, \text{J}
\]

So, the heat required to raise the temperature to the boiling point is **19,548 J**.

### Part b: Converting boiling water to steam
Here, we use the formula for latent heat:
\[
Q = mL
\]
Where:
- \( L \) is the latent heat of vaporization of water (\( L = 2260 \, \text{J/g} \) or \( 2.26 \times 10^6 \, \text{J/kg} \)).

Now calculate the heat required to convert the 100°C water to steam:
\[
Q = (0.060 \, \text{kg})(2.26 \times 10^6 \, \text{J/kg}) = 135,600 \, \text{J}
\]

So, the heat required to convert the water to steam is **135,600 J**.

### Total Heat Required
To find the total heat added to both heat the water to the boiling point and then convert it to steam:
\[
Q_{\text{total}} = 19,548 \, \text{J} + 135,600 \, \text{J} = 155,148 \, \text{J}
\]

### Summary:
- **a.** Heat required to raise the water to boiling point: **19,548 J**.
- **b.** Heat required to convert boiling water to steam: **135,600 J**.

Let me know if you'd like further details or clarifications.

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Here are 5 related questions:
1. How much heat is required to heat 100 g of water from 25°C to 100°C?
2. What is the latent heat of fusion for ice?
3. How does the specific heat capacity of water compare to other substances?
4. How much energy is required to freeze 60 g of water at 0°C?
5. What is the relationship between specific heat and temperature change?

**Tip**: When dealing with phase changes, always account for both the energy needed to change the temperature and the energy for the phase transition.

How much heat must be added to 60 g of water at an initial temperature of 22°C to a) Heat it to the boiling point? b) Completely convert the 100°C water to steam?

Calculate how much heat is needed to raise 60 g of water from 22°C to boiling (100°C) and convert it to steam. Learn about heat transfer, specific heat, and latent heat of vaporization in this detailed step-by-step thermodynamics problem. Suitable for Grades 9-12.

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