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A system uses 49 J of energy to do work, and the change in internal energy is 58 J. How much heat was added to the system?

A. 9 J
B. 97 J
C. 107 J
D. 117 J

Sagot :

GinnyAnswer
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]
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