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Ch.1 Matter and Measurements
Chapter 1, Problem 21

Assuming that Coca-Cola has the same specific heat as water, how much energy in calories is removed when 350 g of Coca-Cola (about the contents of one 12 oz can) is cooled from room temperature ( 25 ° C ) to refrigerator temperature ( 3 ° C )?

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1
Identify the specific heat capacity of water, which is 1 cal/g°C.
Determine the mass of the Coca-Cola, which is given as 350 g.
Calculate the change in temperature (\( \Delta T \)) by subtracting the final temperature (3°C) from the initial temperature (25°C).
Use the formula for heat energy: \( q = m \cdot c \cdot \Delta T \), where \( q \) is the heat energy, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
Substitute the known values into the formula to find the energy removed in calories.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Specific Heat Capacity

Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. For water, this value is approximately 1 calorie/gram °C. In this question, it is assumed that Coca-Cola has the same specific heat as water, which allows us to use this value to calculate the energy change during cooling.
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Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. In this scenario, energy is removed from Coca-Cola as it cools down from room temperature to refrigerator temperature, which involves calculating the heat lost using the formula Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.
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Temperature Change

Temperature change (ΔT) is the difference between the initial and final temperatures of a substance. In this case, the initial temperature is 25 °C and the final temperature is 3 °C, resulting in a temperature change of ΔT = 25 °C - 3 °C = 22 °C. This value is crucial for calculating the total energy removed from the Coca-Cola during the cooling process.
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