Question

using the heat equation to find mass
a piece of copper (c = 0.385 \\(\frac{j}{g\degree c}\\)) undergoing a temperature change from 150\\(\degree\\)c to 225\\(\degree\\)c absorbs 3,500 joules of energy.
what is the mass of the piece of copper? express the answer to the nearest whole number.
\boxed{} grams

Explanation:

Step1: Recall the heat equation

The heat equation is \( Q = mc\Delta T \), where \( Q \) is the heat energy, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

Step2: Calculate the change in temperature

\( \Delta T = T_{final}-T_{initial}=225^{\circ}C - 150^{\circ}C=75^{\circ}C \)

Step3: Rearrange the heat equation to solve for mass

From \( Q = mc\Delta T \), we can solve for \( m \) as \( m=\frac{Q}{c\Delta T} \)

Step4: Substitute the given values into the formula

We know that \( Q = 3500 \) J, \( c = 0.385\frac{J}{g\cdot^{\circ}C} \), and \( \Delta T=75^{\circ}C \). Substituting these values:
\( m=\frac{3500}{0.385\times75} \)
First, calculate the denominator: \( 0.385\times75 = 28.875 \)
Then, calculate the mass: \( m=\frac{3500}{28.875}\approx121.21 \)
Rounding to the nearest whole number, \( m\approx121 \)

Answer:

121