How much heat is required to raise a 50.0 g piece of iron from 25 °C to its melting point of 1538 °C? The specific heat capacity for iron is 0.451 J/g•°C. (a) 34.1 kJ (b) 168 kJ (c) 12.1 kJ (d) 6.78 kJ

검증된 단계별 안내

Identify the given values: mass of iron (m) = 50.0 g, initial temperature (T_initial) = 25 °C, final temperature (T_final) = 1538 °C, and specific heat capacity of iron (c) = 0.451 J/g•°C.

Understand the formula for heat transfer, which is Q = m * c * ΔT, where Q is the heat required, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Calculate the change in temperature (ΔT) by subtracting the initial temperature from the final temperature: ΔT = T_final - T_initial.

Substitute the values into the heat transfer formula: Q = 50.0 g * 0.451 J/g•°C * (1538 °C - 25 °C).

Convert the result from joules to kilojoules by dividing by 1000, as 1 kJ = 1000 J.

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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. It is a material-specific property that indicates how much energy is needed to change the temperature of a substance, which is crucial for calculating heat transfer in thermal processes.

Heat Transfer Calculation

The heat transfer (q) required to change the temperature of a substance can be calculated using the formula q = m × c × ΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. This formula allows us to quantify the energy needed for temperature changes in various materials.

Phase Change and Melting Point

The melting point is the temperature at which a solid becomes a liquid. In this context, understanding the melting point of iron (1538 °C) is essential, as it indicates the temperature to which the iron must be heated. The energy required to reach this temperature from an initial state is calculated using the specific heat capacity.