How much heat is required to warm 1.50 kg of sand from 25.0 °C to 100.0 °C?

검증된 단계별 안내

Identify the specific heat capacity of sand, which is typically around 0.290 J/g°C.

Convert the mass of sand from kilograms to grams. Since 1 kg equals 1000 grams, multiply the mass of the sand by 1000.

Calculate the temperature change (ΔT) by subtracting the initial temperature from the final temperature.

Use the formula for heat (q) required: q = m * c * ΔT, where m is the mass in grams, c is the specific heat capacity, and ΔT is the temperature change.

Substitute the values into the formula to find the amount of 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). This equation is fundamental in calculating the heat required for temperature changes in various materials, allowing for precise energy calculations in thermal processes.

Temperature Change

Temperature change (ΔT) is the difference between the final and initial temperatures of a substance. In this case, it is calculated as 100.0 °C - 25.0 °C, resulting in a ΔT of 75.0 °C. Understanding temperature change is crucial for determining how much heat energy is needed to achieve the desired temperature increase in a material.