Question

At temperatures of a few hundred kelvins, the specific heat capacity of copper approximately follows the empirical formula c=α+βT+δT^(-2), where α=349 J/kg·K, β=0.107 J/kg·K^2, and δ=4.58×10^5 J·kg·K. How much heat is needed to raise the temperature of a 2.00-kg piece of copper from 20°C to 250°C?

a) Calculate the heat using the given formula.
b) The heat required is independent of temperature.
c) The specific heat formula is invalid for copper.
d) Heat cannot be determined without additional information.

Answer 1

To calculate the heat needed to raise the temperature of copper, use the given formula and convert the mass to grams. Then, calculate the change in temperature and plug the values into the formula to find the specific heat capacity. Finally, multiply the specific heat capacity by the mass and change in temperature to calculate the heat needed.

Step-by-step explanation:

To calculate the heat needed to raise the temperature of the copper, we can use the given formula c=α+βT+δT^(-2), where α=349 J/kg·K, β=0.107 J/kg·K^2, and δ=4.58×10^5 J·kg·K. First, we need to convert the mass of the copper from kilograms to grams by multiplying it by 1000 (2.00 kg x 1000 g/kg = 2000 g). Next, we calculate the change in temperature by subtracting the initial temperature from the final temperature (250°C - 20°C = 230°C). Plugging these values into the formula, we get c = 349 + 0.107(230) + 4.58×10^5/(230)^2. Simplifying the equation gives us the specific heat capacity of copper. Finally, we can calculate the heat needed by multiplying the specific heat capacity by the mass of copper and the change in temperature (Q = c x m x ΔT).