Question

practice activity # 3
solve the following problem. show complete details of your answers.
how much heat is required to change 500g of water at 100 °c into vapor at 108

Explanation:

To solve the problem of finding the heat required to change 500 g of water at \( 100^\circ \text{C} \) into vapor at \( 108^\circ \text{C} \), we need to consider two processes:

1. Phase change (vaporization): Converting water at \( 100^\circ \text{C} \) to steam at \( 100^\circ \text{C} \).
2. Sensible heating: Heating the steam from \( 100^\circ \text{C} \) to \( 108^\circ \text{C} \).

Step 1: Phase Change (Vaporization)

The heat required for vaporization is given by:
\[ Q_1 = m \cdot L_v \]
where:

• \( m = 500 \, \text{g} = 0.5 \, \text{kg} \) (mass of water),
• \( L_v = 2.26 \times 10^6 \, \text{J/kg} \) (latent heat of vaporization of water).

Substitute the values:
\[ Q_1 = 0.5 \, \text{kg} \times 2.26 \times 10^6 \, \text{J/kg} \]
\[ Q_1 = 1.13 \times 10^6 \, \text{J} \]

Step 2: Sensible Heating of Steam

The heat required to raise the temperature of steam is given by:
\[ Q_2 = m \cdot c_{\text{steam}} \cdot \Delta T \]
where:

• \( c_{\text{steam}} = 2010 \, \text{J/(kg·°C)} \) (specific heat capacity of steam),
• \( \Delta T = 108^\circ \text{C} - 100^\circ \text{C} = 8^\circ \text{C} \) (temperature change).

Substitute the values:
\[ Q_2 = 0.5 \, \text{kg} \times 2010 \, \text{J/(kg·°C)} \times 8^\circ \text{C} \]
\[ Q_2 = 0.5 \times 2010 \times 8 \, \text{J} \]
\[ Q_2 = 8040 \, \text{J} \]

Step 3: Total Heat Required

Add \( Q_1 \) and \( Q_2 \) to get the total heat:
\[ Q_{\text{total}} = Q_1 + Q_2 \]
\[ Q_{\text{total}} = 1.13 \times 10^6 \, \text{J} + 8040 \, \text{J} \]
\[ Q_{\text{total}} = 1138040 \, \text{J} \approx 1.14 \times 10^6 \, \text{J} \]

Answer:

The total heat required is approximately \( \boldsymbol{1.14 \times 10^6 \, \text{J}} \) (or \( 1138040 \, \text{J} \)).