Certainly! Let's go through the problem step-by-step using the principles of thermodynamics.
We start with the First Law of Thermodynamics, which is given by:
[tex]\[
\Delta U = Q - W
\][/tex]
where:
- [tex]\(\Delta U\)[/tex] is the change in internal energy of the system.
- [tex]\(Q\)[/tex] is the heat added to the system.
- [tex]\(W\)[/tex] is the work done by the system.
### Step-by-Step Solution:
1. Identify the given values:
- The work done by the system, [tex]\(W\)[/tex], is [tex]\(49 J\)[/tex].
- The change in internal energy, [tex]\(\Delta U\)[/tex], is [tex]\(58 J\)[/tex].
2. Rearrange the First Law of Thermodynamics to solve for [tex]\(Q\)[/tex]:
[tex]\[
Q = \Delta U + W
\][/tex]
3. Substitute the given values into the equation:
[tex]\[
Q = 58 J + 49 J
\][/tex]
4. Calculate the heat added to the system:
[tex]\[
Q = 107 J
\][/tex]
Therefore, the amount of heat added to the system is:
[tex]\[
107 J
\][/tex]
Given the multiple choices, the correct answer is:
[tex]\[
107 J
\][/tex]
