How much heat is required to warm 1.50 L of water from 25.0 °C to 100.0 °C? (Assume a density of 1.0 g/mL for the water.)

검증된 단계별 안내

Calculate the mass of the water using its volume and density. Since the density of water is 1.0 g/mL, convert the volume from liters to milliliters and then to grams.

Use the specific heat capacity of water, which is 4.18 J/g°C, to set up the heat equation: q = m * c * ΔT, where q is the heat absorbed, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Determine the change in temperature (ΔT) by subtracting the initial temperature (25.0 °C) from the final temperature (100.0 °C).

Substitute the values for mass, specific heat capacity, and change in temperature into the heat equation.

Solve the equation to find the amount of heat required to warm the water from 25.0 °C to 100.0 °C.

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주요 개념

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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 required to change the temperature of water, as it directly relates the mass of the water and the temperature change to the total heat absorbed or released.

Mass Calculation from Volume

To calculate the mass of water from its volume, we use the relationship between density, mass, and volume. Given that the density of water is 1.0 g/mL, 1.50 L of water (which is 1500 mL) has a mass of 1500 grams. This conversion is essential for determining how much heat is needed, as the mass of the water directly influences the total heat calculation.

Heat Transfer Equation

The heat transfer equation, often expressed as q = mcΔT, relates the heat (q) absorbed or released to the mass (m) of the substance, its specific heat capacity (c), and the change in temperature (ΔT). In this scenario, ΔT is the difference between the final and initial temperatures of the water. This equation is fundamental for solving the problem, as it allows us to calculate the total heat required to warm the water from 25.0 °C to 100.0 °C.