A system does 210 J of work on its environment and gains 80.6 J of heat in the process. Find the change in the internal energy of (a) the system and (b) the environment.
ÄU = Q - W
Where ÄU is the change in the internal energy of the system,
Q is the heat/energy gained from the surroundings,
W is the work done on the environment.
ÄU =80.6-210=-129.4 J.
The internal energy decreased by 129.4 Joules which corresponds to a temperature decrease of the system
I understand what the internal energy of the system is but I do not understand how to find the environment.
Enviromentenergy=- change in internalwork Rationale: if the internal energy increased by xXXX, then the environment must have lost that much energy.
To determine the change in the internal energy of the environment, you can use the fact that energy is conserved in a closed system. In other words, the total change in energy of the system and the environment must add up to zero.
Since the system gained 80.6 J of heat and did 210 J of work on the environment, the change in internal energy of the system is -129.4 J (as you correctly calculated).
Since the total change in energy is zero, the change in internal energy of the environment would be the opposite of the change in internal energy of the system. In this case, it would be 129.4 J (with the opposite sign).
So, to summarize:
- The change in internal energy of the system is -129.4 J (indicating a decrease in internal energy).
- The change in internal energy of the environment is 129.4 J (indicating an increase in internal energy).
This means that the system transferred energy to the environment, resulting in a decrease in the system's internal energy and an increase in the environment's internal energy.