Multiple Choice
How much heat, in kJ, is required to warm 1.59 L of water from 23.7 °C to 79.5 °C? The specific heat of water is 4.184 J/g°C. Assume a density of 1.00 g/mL for water.
8. Thermochemistry
Heat Capacity
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Suppose that 0.44 g of water at 25 °C condenses on the surface of a 51-g block of aluminum that is initially at 25 °C. If the heat released during condensation goes only toward heating the metal, what is the final temperature (in °C)?
A
28.7 °C
B
32.1 °C
C
30.2 °C
D
26.5 °C
Verified step by step guidance1
First, understand that when water condenses, it releases heat. This heat will be absorbed by the aluminum block, causing its temperature to rise.
Calculate the heat released during the condensation of water using the formula: \( q = m \cdot \Delta H_{\text{vap}} \), where \( m \) is the mass of the water and \( \Delta H_{\text{vap}} \) is the heat of vaporization of water. For water, \( \Delta H_{\text{vap}} \) is approximately 2260 J/g.
Next, use the heat absorbed by the aluminum to find the change in temperature. The formula to use is: \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of the aluminum, \( c \) is the specific heat capacity of aluminum (approximately 0.897 J/g°C), and \( \Delta T \) is the change in temperature.
Set the heat released by the water equal to the heat absorbed by the aluminum: \( m_{\text{water}} \cdot \Delta H_{\text{vap}} = m_{\text{aluminum}} \cdot c \cdot \Delta T \). Solve for \( \Delta T \).
Finally, add the change in temperature \( \Delta T \) to the initial temperature of the aluminum block (25 °C) to find the final temperature.
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