(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?

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.