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)?

Verified step by step guidance

1. Step 1: Recall the formula for calculating heat energy: $Q\; =\; m\; \times \; c\; \times \; \Delta T$, where $Q$ is the heat energy, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature.
2. Step 2: Identify the given values: mass $m\; =\; 350\; \backslash ,\; g$, specific heat capacity of water $c\; =\; 1.00\; \backslash ,\; cal/(g\; \backslash ,\; °C)$, initial temperature $T\_\{initial\}\; =\; 25\; \backslash ,\; °C$, and final temperature $T\_\{final\}\; =\; 3\; \backslash ,\; °C$.
3. Step 3: Calculate the temperature change $\Delta T$ using the formula $\Delta T\; =\; T\_\{final\}\; -\; T\_\{initial\}$. Substitute the values: $\Delta T\; =\; 3\; \backslash ,\; °C\; -\; 25\; \backslash ,\; °C$.
4. Step 4: Substitute the values for $m$, $c$, and $\Delta T$ into the heat energy formula $Q\; =\; m\; \times \; c\; \times \; \Delta T$. This becomes $Q\; =\; 350\; \backslash ,\; g\; \times \; 1.00\; \backslash ,\; cal/(g\; \backslash ,\; °C)\; \times \; \Delta T$.
5. Step 5: Simplify the expression to find the total heat energy $Q$. Remember that the result will be in calories, and the negative sign indicates that energy is being removed (cooled).

Key Concepts

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 this problem, it is assumed that Coca-Cola has the same specific heat as water, which is approximately 1 cal/g°C. This concept is crucial for calculating the energy change when the temperature of a substance changes.

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.

Temperature Change

Temperature change is the difference in temperature between two states of a substance. In this case, the temperature change (ΔT) is calculated by subtracting the final temperature (3 °C) from the initial temperature (25 °C), resulting in a ΔT of 22 °C. This value is essential for determining the total energy removed from the Coca-Cola during the cooling process.