Ch.1 Matter and Measurements

McMurry - Fundamentals of General, Organic, and Biological Chemistry 8th Edition

McMurry8th EditionFundamentals of General, Organic, and Biological ChemistryISBN: 9780134015187당신이 사용하는 게 아니라요?교과서 변경

McMurry 8th Edition

Ch.1 Matter and Measurements

문제 21

1장, 문제 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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Step 1: Recall the formula for calculating heat energy:

Q = m × c × ΔT

, where

Q

is the heat energy,

m

is the mass,

c

is the specific heat capacity, and

ΔT

is the change in temperature.

Step 2: Identify the given values: mass

m = 350 \, g

, specific heat capacity of water

c = 1.00 \, cal/(g \, °C)

, initial temperature

T_{initial} = 25 \, °C

, and final temperature

T_{final} = 3 \, °C

Step 3: Calculate the temperature change

ΔT

using the formula

ΔT = T_{final} - T_{initial}

. Substitute the values:

ΔT = 3 \, °C - 25 \, °C

Step 4: Substitute the values for

m

c

, and

ΔT

into the heat energy formula

Q = m × c × ΔT

. This becomes

Q = 350 \, g × 1.00 \, cal/(g \, °C) × ΔT

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).

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주요 개념

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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.