A system does 196 J of work on its environment and gains 40 J of heat in the process.
(a) What is the change in the internal energy of the system?
J
(b) What is the change in the internal energy of the environment?
J
I thought the answer would be +40 for the system and -40 for the enveironment sin the system gain 40 j of heat, but that is not the correct answer. What am I doing wrong.
Work done by the system is -.
It seems to me that the system does 196 J work so that is -196 J. It receives 40 J of heat which is +. Therefore, -196+40 would be the change. The environment would be the negative of that. Check my thinking.
In order to determine the changes in internal energy for the system and the environment, we need to apply the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the sum of the work done on the system and the heat added to the system.
(a) Change in internal energy of the system:
ΔU(system) = Q - W
Here, Q represents the heat added to the system, and W represents the work done on the system.
Given that the system does 196 J of work on its environment and gains 40 J of heat, we have:
W = 196 J
Q = 40 J
ΔU(system) = 40 J - 196 J
ΔU(system) = -156 J
Therefore, the change in internal energy of the system is -156 J.
(b) Change in internal energy of the environment:
Since the system does work on its environment and gains heat, the change in internal energy of the environment will be the opposite of the change in internal energy of the system.
ΔU(environment) = -ΔU(system)
ΔU(environment) = -(-156 J) [negating the negative value]
ΔU(environment) = 156 J
Therefore, the change in internal energy of the environment is 156 J.
Your initial assumption was incorrect because you mistakenly considered the change in heat as the change in internal energy. The change in internal energy is the sum of heat and work, and its value depends on the direction (positive or negative) of both.