A cube of iron $\left(C_p=0.450 J / g \cdot{ }^{\circ} C \right)$ with a mass of 55.8 g is heated from $25.0^{\circ} C$ to $49.0^{\circ} C$. How much heat is required for this process? Round your answer to three significant figures. Use the formula $q=m C_y \Delta T$.
Answer (2)
Calculate the change in temperature: Δ T = 49.0 − 25.0 = 24. 0 ∘ C .
Use the formula q = m C p Δ T to calculate the heat required.
Substitute the given values: q = 55.8 × 0.450 × 24.0 = 602.64 J .
Round the result to three significant figures: 603 J.
Explanation
Problem Setup and Given Data We are given a cube of iron with a specific heat capacity C p = 0.450 J / g ⋅ ∘ C , a mass m = 55.8 g , and it is heated from an initial temperature T i = 25. 0 ∘ C to a final temperature T f = 49. 0 ∘ C . We need to find the amount of heat required for this process using the formula q = m C p Δ T .
Calculating the Change in Temperature First, we need to calculate the change in temperature, which is the difference between the final and initial temperatures: Δ T = T f − T i = 49. 0 ∘ C − 25. 0 ∘ C = 24. 0 ∘ C
Calculating the Heat Required Now, we can calculate the heat required using the formula q = m C p Δ T : q = ( 55.8 g ) × ( 0.450 J / g ⋅ ∘ C ) × ( 24. 0 ∘ C ) = 602.64 J
Rounding to Three Significant Figures Finally, we need to round the answer to three significant figures. Since the calculated value is 602.64 J, rounding to three significant figures gives us 603 J.
Final Answer Therefore, the amount of heat required for this process is 603 J.
Examples
Imagine you're heating a metal component in an engine to test its thermal properties. Knowing the specific heat capacity, mass, and temperature change allows you to calculate the exact amount of heat energy needed. This calculation is crucial for designing efficient cooling systems, predicting material behavior under different temperatures, and ensuring the engine's reliability. By understanding these principles, engineers can optimize engine performance and prevent overheating, leading to safer and more durable machines.
The heat required to heat a 55.8 g cube of iron from 25.0 °C to 49.0 °C is calculated using the formula q = m C_p ΔT. After calculating the temperature change and substituting the values into the formula, the required heat was found to be 603 J. This result is rounded to three significant figures from 602.64 J.
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