How much heat is required to warm 2.50 kg of sand from 25.0 °C to 100.0 °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 sand, which is given as 2.50 kg.

Find the specific heat capacity \( c \) of sand. For sand, \( c \) is approximately 0.84 J/g°C. Convert this to J/kg°C by multiplying by 1000, resulting in 840 J/kg°C.

Calculate the change in temperature \( \Delta T \) by subtracting the initial temperature from the final temperature: \( \Delta T = 100.0 \text{ °C} - 25.0 \text{ °C} \).

Substitute the values into the formula: \( q = 2.50 \text{ kg} \times 840 \text{ J/kg°C} \times \Delta T \) to find the heat required.

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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 kilogram of a substance by one degree Celsius. It is a material-specific property that varies between different substances. For sand, the specific heat capacity is approximately 0.84 J/g°C, which means it requires this amount of energy to increase its temperature.

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). In this equation, ΔT is calculated as the final temperature minus the initial temperature. This formula is essential for calculating the heat required to change the temperature of a substance.

Units of Measurement

Understanding units of measurement is crucial in chemistry calculations. Heat is typically measured in joules (J) or calories, while mass is measured in kilograms (kg) or grams (g). When using the specific heat capacity in calculations, it is important to ensure that all units are consistent, particularly when converting between kilograms and grams or between Celsius and Kelvin.