In a heat engine, if 700 J of heat enters the system, and the piston does 400 J of work, what is the final internal (thermal) energy of the system if the initial energy is 1,200 J?
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To find the final internal energy of the system, we need to consider the law of energy conservation. Energy is neither created nor destroyed, so the change in internal energy of the system is equal to the net heat energy added to the system minus the work done by the system.
The formula for the change in internal energy is given by:
ΔU = Q - W
where:
ΔU = change in internal energy
Q = heat energy added to the system
W = work done by the system
In this case, Q is 700 J (heat entering the system) and W is -400 J (negative because work is done by the system). Plugging these values into the equation, we have:
ΔU = 700 J - (-400 J)
ΔU = 700 J + 400 J
ΔU = 1,100 J
The change in internal energy of the system is 1,100 J.
To find the final internal energy, we need to add this change to the initial internal energy:
Final Internal Energy = Initial Internal Energy + ΔU
Final Internal Energy = 1,200 J + 1,100 J
Final Internal Energy = 2,300 J
Therefore, the final internal energy of the system is 2,300 J.