A system does 137 J of work on its environment and gains 95.3 J of heat in the process. Find the change in the internal energy of (a) the system and (b) the environment
To find the change in internal energy, we can use the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
(a) Change in internal energy of the system:
ΔU = Q - W
= 95.3 J - 137 J
= -41.7 J
The change in internal energy of the system is -41.7 J, indicating a decrease in internal energy.
(b) Change in internal energy of the environment:
According to the conservation of energy, the change in internal energy of the environment is equal in magnitude but opposite in sign to the change in internal energy of the system.
ΔU_environment = -ΔU_system
= -(-41.7 J)
= 41.7 J
The change in internal energy of the environment is 41.7 J, indicating an increase in internal energy.
To find the change in internal energy of the system, we can use the First Law of Thermodynamics:
ΔU = Q - W
Where:
ΔU is the change in internal energy of the system
Q is the heat added to the system
W is the work done by the system
Given:
Q = 95.3 J (heat gained by the system)
W = -137 J (work done by the system, negative because work is done on the environment)
Let's substitute the given values into the formula:
ΔU = 95.3 J - (-137 J)
ΔU = 95.3 J + 137 J
ΔU = 232.3 J
Therefore, the change in internal energy of the system is 232.3 J.
To find the change in internal energy of the environment, we need to consider that the system is doing work on the environment, which means the environment is gaining energy. The change in internal energy of the environment is equal to the negative of the work done by the system:
ΔU_environment = -W = -(-137 J) = 137 J
Therefore, the change in internal energy of the environment is 137 J.