(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?

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Identify the formula to calculate the heat required: \( q = m \cdot c \cdot \Delta T \), where \( q \) is the heat energy, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

Determine the mass \( m \) of the water, which is given as 5.00 kg.

Use the specific heat capacity \( c \) of liquid water, which is typically \( 4.18 \text{ J/g°C} \). Convert this to \( \text{kJ/kg°C} \) if necessary.

Calculate the change in temperature \( \Delta T \) by subtracting the initial temperature from the final temperature: \( \Delta T = 46.2°C - 24.6°C \).

Substitute the values into the formula to find \( q \): \( q = 5.00 \text{ kg} \times 4.18 \text{ kJ/kg°C} \times \Delta T \).

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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 one gram of a substance by one degree Celsius. For water, this value is approximately 4.18 J/g°C. Understanding this concept is crucial for calculating the heat energy needed for temperature changes in substances.

Heat Transfer Equation

The heat transfer equation, often expressed as q = mcΔT, relates the heat energy (q) absorbed or released by a substance to its mass (m), specific heat capacity (c), and the change in temperature (ΔT). This equation is fundamental for solving problems involving temperature changes in materials.

Units of Energy

Energy is commonly measured in joules (J) or kilojoules (kJ), where 1 kJ equals 1000 J. In thermodynamics, it is important to be consistent with units when performing calculations, especially when converting between different energy units to ensure accurate results.

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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. (b) What can you say about the specific heats of A and B?

Textbook Question

(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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Textbook Question

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

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The specific heat of octane, C₈H₁₈(l), is 2.22 J•g/K. (a) How many J of heat are needed to raise the temperature of 80.0 g of octane from 10.0 to 25.0 °C?

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The specific heat of octane, C₈H₁₈(l), is 2.22 J•g/K. (b) Which will require more heat, increasing the temperature of 1 mol of C₈H₁₈(l), by a certain amount or increasing the temperature of 1 mol of H₂O(l) by the same amount?