Certainly! Let's solve the problem step-by-step:
1. Identify the given values:
- [tex]\( Q \)[/tex]: The thermal energy released from the system.
- [tex]\( W \)[/tex]: The work done by the system on the surroundings.
From the problem statement:
- [tex]\( Q = -30 \, \text{J} \)[/tex] (since the thermal energy is released from the system, it is negative)
- [tex]\( W = 40 \, \text{J} \)[/tex] (the work done by the system on the surroundings is positive)
2. Use the formula for the change in internal energy:
[tex]\[
\Delta U = Q - W
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
\Delta U = -30 \, \text{J} - 40 \, \text{J}
\][/tex]
4. Calculate the change in internal energy:
[tex]\[
\Delta U = -30 \, \text{J} - 40 \, \text{J} = -70 \, \text{J}
\][/tex]
So, the change in internal energy ([tex]\(\Delta U\)[/tex]) is [tex]\( -70 \, \text{J} \)[/tex].
Therefore, the correct answer is:
D. [tex]\( -70 \, \text{J} \)[/tex]
