The specific heat of copper metal is 0.385 J/g.°C. How many joules of heat are required to raise the temperature of a 2.63 g block of copper from 25.0°C to 79.7 °C?
Report your answer with the correct number of significant figures in regular form. Do not include units in your answer.
Answer (2)
Calculate the change in temperature: Δ T = 79.7° C − 25.0° C = 54.7° C .
Use the formula Q = m c Δ T to find the heat required.
Substitute the values: Q = ( 2.63 g ) × ( 0.385 J/g°C ) × ( 54.7 °C ) = 55.386485 J .
Round the result to 3 significant figures: 55.4
Explanation
Problem Overview We are given the specific heat of copper, the mass of a copper block, and the initial and final temperatures. We need to find the amount of heat required to raise the temperature of the copper block.
Heat Transfer Formula We will use the formula Q = m c Δ T , where:
Q is the heat required (in joules), m is the mass of the substance (in grams), c is the specific heat capacity of the substance (in J/g°C), Δ T is the change in temperature (in °C).
Calculating Temperature Change First, we need to calculate the change in temperature, Δ T :
Δ T = T f ina l − T ini t ia l = 79.7° C − 25.0° C = 54.7° C
Substituting Values Now, we can substitute the given values into the formula:
Q = ( 2.63 g ) × ( 0.385 J/g°C ) × ( 54.7 °C )
Calculating Heat Required Calculating the heat required:
Q = 2.63 × 0.385 × 54.7 = 55.386485 J
Rounding to Significant Figures We need to round the answer to the correct number of significant figures. The least number of significant figures in the given values is 3 (from 2.63 and 0.385). Therefore, we round the result to 3 significant figures:
Q ≈ 55.4 J
Final Answer Therefore, the amount of heat required to raise the temperature of the copper block is 55.4 J.
Examples
Heat capacity is an important concept in many real-world applications. For example, when designing engines, engineers need to consider the heat capacity of the materials used to build the engine. If a material with a low heat capacity is used, the engine may overheat. Similarly, when designing buildings, architects need to consider the heat capacity of the materials used to construct the building. Materials with high heat capacity can help to keep the building cool in the summer and warm in the winter, reducing energy costs. This principle is also used in cooking, where different materials heat up at different rates depending on their specific heat capacities.
To raise the temperature of a 2.63 g block of copper from 25.0 °C to 79.7 °C, 55.4 joules of heat are required. This is calculated using the specific heat formula Q = mcΔT, where the change in temperature is found to be 54.7 °C. The final answer is rounded to three significant figures.
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