Multiple Choice
How much would the temperature of 309 g of ethanol increase if 25.3 kJ of heat were added to it? The specific heat of ethanol is 2.42 J/g°C.
8. Thermochemistry
Heat Capacity
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In a process where 4.80 kg of boiling water is used to raise the temperature of 25.0 kg of water in a bath to body temperature, how much heat is transferred if the heat lost by the boiling water is equal to the heat gained by the room-temperature water?
A
10.08 kJ
B
4800 kJ
C
2010 kJ
D
0.504 kJ
Verified step by step guidance1
Identify the principle of conservation of energy, which states that the heat lost by the boiling water is equal to the heat gained by the room-temperature water.
Use the formula for heat transfer: \( q = m \cdot c \cdot \Delta T \), where \( q \) is the heat transferred, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
Determine the specific heat capacity of water, which is typically \( 4.18 \text{ J/g°C} \).
Calculate the change in temperature (\( \Delta T \)) for both the boiling water and the room-temperature water. For boiling water, \( \Delta T \) is the difference between 100°C and the final temperature. For the room-temperature water, \( \Delta T \) is the difference between the final temperature and the initial temperature.
Set up the equation \( m_1 \cdot c \cdot \Delta T_1 = m_2 \cdot c \cdot \Delta T_2 \) and solve for the unknown, ensuring that the units are consistent throughout the calculation.
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