Questions: Consider a 290 g sample of water. How much energy is absorbed as the water is heated from 14.0°C to 90.0°C? Be sure each of your answer entries has the correct number of significant figures. Note: Reference the Phase change properties of pure substances and Conversion factors for non-SI units tables for additional information. Part 1 of 3 Report the energy absorbed in joules. J

Solution Steps

We have a 290 g sample of water, and we need to calculate the energy absorbed as it is heated from \(14.0^{\circ} \mathrm{C}\) to \(90.0^{\circ} \mathrm{C}\).

The formula to calculate the energy absorbed when heating a substance is: \[ q = m \cdot c \cdot \Delta T \] where:

• \(q\) is the heat absorbed (in joules),
• \(m\) is the mass of the substance (in grams),
• \(c\) is the specific heat capacity of the substance (for water, \(c = 4.184 \, \text{J/g}^\circ\text{C}\)),
• \(\Delta T\) is the change in temperature (in degrees Celsius).

The change in temperature \(\Delta T\) is given by: \[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 90.0^{\circ} \mathrm{C} - 14.0^{\circ} \mathrm{C} = 76.0^{\circ} \mathrm{C} \]

Substitute the values into the formula: \[ q = 290 \, \text{g} \times 4.184 \, \text{J/g}^\circ\text{C} \times 76.0^{\circ} \mathrm{C} \] \[ q = 92211.52 \, \text{J} \]

The mass of the water (290 g) and the temperature change (76.0°C) both have three significant figures, so the energy absorbed should also be reported with three significant figures: \[ q = 9.22 \times 10^4 \, \text{J} \]

Final Answer