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)
A. 21900 J
B. 627.0 J
C. 125.4 J
D. 28200 J

Answer 1

To calculate the amount of energy needed to raise the temperature of water, you can use the formula:

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

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

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

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

\[
\Delta T = T_f - T_i = 45.0°C - 10.0°C = 35.0°C
\]

Now, plug all values into the formula:

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

Calculating \( q \):

\[
q = 150.0 \cdot 4.18 \cdot 35.0
\]

First calculate \( 150.0 \cdot 4.18 \):

\[
150.0 \cdot 4.18 = 627.0
\]

Now calculate \( 627.0 \cdot 35.0 \):

\[
627.0 \cdot 35.0 = 21945.0 \, \text{J}
\]

So the amount of energy needed is approximately \( 21945.0 \, \text{J} \). Rounding to significant figures based on the inputs (which are three significant figures for mass and temperature), we say:

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

Thus, the correct answer is:

**A. 21900 J**