Question

What amount of energy is needed to raise the temperature of 150.0 g of water from 10.0°C to 45.0°C? (Given: Cwater = 4.18 J/g • °C)(1 point)
Responses

21900 J
21900 J

125.4 J
125.4 J

28200 J
28200 J

627.0 J

Answer 1

To calculate the amount of energy required to raise the temperature of water, we use the formula:

\[ q = m \cdot C \cdot \Delta T \]

where:
- \( q \) is the amount of heat energy (in Joules),
- \( m \) is the mass of the substance (in grams),
- \( C \) is the specific heat capacity (in J/g·°C),
- \( \Delta T \) is the change in temperature (in °C).

Given:
- Mass of water, \( m = 150.0 \, \text{g} \)
- Specific heat capacity of water, \( C = 4.18 \, \text{J/g·°C} \)
- Initial temperature, \( T_i = 10.0 \, \text{°C} \)
- Final temperature, \( T_f = 45.0 \, \text{°C} \)

First, we need to calculate the change in temperature, \( \Delta T \):

\[ \Delta T = T_f - T_i = 45.0 \, \text{°C} - 10.0 \, \text{°C} = 35.0 \, \text{°C} \]

Now, we can substitute the values into the formula:

\[ q = 150.0 \, \text{g} \cdot 4.18 \, \text{J/g·°C} \cdot 35.0 \, \text{°C} \]

Calculating \( q \):

\[ q = 150.0 \cdot 4.18 \cdot 35.0 = 21930 \, \text{J} \]

Rounding to three significant figures, we get:

\[ q \approx 21900 \, \text{J} \]

Thus, the amount of energy needed to raise the temperature of 150.0 g of water from 10.0°C to 45.0°C is **21900 J**.