A domestic refrigerator is loaded with food and door is closed. During acertain period the machine consumes 1kWh of energy and internal energy ofthe system drops by 5000kJ. Find the net heat transfer for the system
Question
A domestic refrigerator is loaded with food and door is closed. During acertain period the machine consumes 1kWh of energy and internal energy ofthe system drops by 5000kJ. Find the net heat transfer for the system
Solution
To solve this problem, we need to 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.
Step 1: Convert all quantities to the same units. Here, we'll use Joules. 1 kWh is equal to 3.6 million Joules (J). So, the machine consumes 3.6 million J of energy. The internal energy of the system drops by 5000 kJ, which is equal to 5 million J.
Step 2: Apply the first law of thermodynamics. The change in internal energy (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W). In this case, the work done by the system is the energy consumed by the refrigerator, and the change in internal energy is a decrease of 5 million J. So, we have:
-5,000,000 J = Q - 3,600,000 J
Step 3: Solve for Q. Add 3,600,000 J to both sides of the equation to isolate Q:
Q = -5,000,000 J + 3,600,000 J = -1,400,000 J
So, the net heat transfer for the system is -1,400,000 J. The negative sign indicates that heat is being removed from the system, which makes sense for a refrigerator.
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