A system has an initial energy of 117 joules. The energy equation includes --40.1 J of heat and -20.3 J of work. What is the final energy? Was heat added to the system or to the environment? Was work done by the system or to the system? Be sure to show all of your work and include the correct units.

E = q + w

117J = -40.1J + (-20.3 J)
This doesn't add to 117; I don't understand the problem. Perhaps another tutor can help.

To determine the final energy of the system, we need to use the energy equation:

ΔE = Q + W

where:
ΔE is the change in energy of the system,
Q is the heat added to the system, and
W is the work done on the system.

Given that the initial energy (E initial) is 117 J, the heat (Q) is -40.1 J, and the work (W) is -20.3 J, we will substitute these values into the energy equation to find the change in energy:

ΔE = Q + W
ΔE = (-40.1 J) + (-20.3 J)
ΔE = -40.1 J - 20.3 J
ΔE = -60.4 J

The negative sign indicates a decrease in energy. Therefore, the final energy of the system is:

E final = E initial + ΔE
E final = 117 J + (-60.4 J)
E final = 56.6 J

Hence, the final energy of the system is 56.6 J.

Now, let's determine whether heat was added to the system or the environment. The negative sign attached to the heat value (-40.1 J) indicates that heat was lost or removed from the system. Therefore, the heat (-40.1 J) was released to the environment.

Next, let's determine if work was done by the system or to the system. The negative sign attached to the work value (-20.3 J) indicates work done on the system. Therefore, work (-20.3 J) was done to the system.

In conclusion:
- The final energy of the system is 56.6 J.
- The heat (-40.1 J) was released to the environment.
- Work (-20.3 J) was done to the system.