(a) What amount of heat (in joules) is required to raise the temperature of 1 g of water by 1 kelvin? (b) What amount of heat (in joules) is required to raise the temperature of 1 mole of water by 1 kelvin?

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Step 1: Understand the concept of specific heat capacity. The specific heat capacity of a substance is the amount of heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius (or 1 Kelvin). For water, this value is approximately 4.18 J/g·K.

Step 2: Calculate the heat required for 1 gram of water. Since the specific heat capacity of water is 4.18 J/g·K, the amount of heat required to raise the temperature of 1 gram of water by 1 Kelvin is simply 4.18 joules.

Step 3: Determine the molar mass of water. Water (H₂O) has a molar mass of approximately 18.02 g/mol. This means 1 mole of water weighs 18.02 grams.

Step 4: Calculate the heat required for 1 mole of water. To find the heat required to raise the temperature of 1 mole of water by 1 Kelvin, multiply the specific heat capacity by the molar mass of water: \( q = 4.18 \text{ J/g·K} \times 18.02 \text{ g/mol} \).

Step 5: Simplify the expression to find the total heat in joules for 1 mole of water. This will give you the amount of heat required to raise the temperature of 1 mole of water by 1 Kelvin.

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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 required to raise the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin). For water, this value is approximately 4.18 J/g·K, meaning it takes 4.18 joules to increase the temperature of 1 gram of water by 1 Kelvin. This concept is crucial for calculating heat transfer in thermal processes.

Molar Heat Capacity

Molar heat capacity refers to the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius (or one Kelvin). For water, the molar heat capacity is about 75.3 J/mol·K. This concept is important when dealing with larger quantities of a substance, as it allows for calculations based on moles rather than mass.

Heat Transfer

Heat transfer is the process of thermal energy moving from one object or substance to another due to a temperature difference. In the context of the question, it involves calculating the heat required to change the temperature of water, which can be determined using the specific or molar heat capacities. Understanding heat transfer is essential for solving problems related to thermal energy changes in substances.

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Heat Capacity

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Textbook Question

(b) The specific heat of aluminum is 0.9 J/(g - K). Calculate its molar heat capacity.

Textbook Question

Two solid objects, A and B, are placed in boiling water and allowed to come to the temperature of the water. Each is then lifted out and placed in separate beakers containing 1000 g of water at 10.0 °C. Object A increases the water temperature by 3.50 °C; B increases the water temperature by 2.60 °C. (a) Which object has the larger heat capacity?

Textbook Question

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Textbook Question

(d) How many kJ of heat are needed to raise the temperature of 5.00 kg of liquid water from 24.6 to 46.2 °C?

Textbook Question

(b) Calculate the energy needed for this temperature change.