Question

# A gas in a closed container is heated with $$10 \,J$$ of energy, causing the lid of the container to rise $$2m$$ with $$3N$$ of force. What is the total change in energy of the system ?

A
10J
B
4J
C
10J
D
4J

Solution

## The correct option is C $$4 \,J$$Explanation:For this problem, use the first law of thermodynamics. The change in energy equals the increase in heat energy minus the work done.$$\Delta U = Q - W$$We are not given a value for work, but we can solve for it using the force and distance. Work is the product of force and displacement.$$W = F \Delta x$$$$W = 3N \times 2m$$$$W = 6\,J$$Now that we have the value of work done and the value for heat added, we can solve for the total change in energy.$$\Delta U = Q - W$$$$\Delta U = 10\,J - 6\,J$$$$\Delta U = 4\,J$$Physics

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