To solve the given problem step-by-step, we need to calculate the change in thermal energy for a process where the system absorbs heat and performs work on the surroundings. We'll use the following formula:
[tex]\[ \Delta E_{thermal} = q + w \][/tex]
where:
- [tex]\( q \)[/tex] is the heat absorbed by the system
- [tex]\( w \)[/tex] is the work done by the system
According to the problem, the system absorbs 140 J of heat from the surroundings and does 85 J of work on the surroundings. Let's identify each component:
- [tex]\( q = 140 \)[/tex] J (heat absorbed)
- [tex]\( w = 85 \)[/tex] J (work done)
Now, plug these values into the formula to find the change in thermal energy:
[tex]\[ \Delta E_{thermal} = q + w \][/tex]
Substitute the known values into the equation:
[tex]\[ \Delta E_{thermal} = 140 \text{ J} + 85 \text{ J} \][/tex]
Perform the addition:
[tex]\[ \Delta E_{thermal} = 225 \text{ J} \][/tex]
Therefore, the change in the thermal energy for the process is:
[tex]\[ \Delta E_{thermal} = 225 \text{ J} \][/tex]
