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  • A gas confined within a piston-cylinder arrangement undergoes a thermody- namic process. Initially, the gas has an internal energy of 1500 J, and the sys-tem performs 400 J of work on its surroundi

A gas confined within a piston-cylinder arrangement undergoes a thermody- namic process. Initially, the gas has an internal energy of 1500 J, and the sys-tem performs 400 J of work on its surroundings while releasing 300 J of heat.Determine the final internal energy of the gas.

Option: 1

140 J


Option: 2

170 J


Option: 3

2200 J


Option: 4

230.0 J


Answers (1)

best_answer

The first law of thermodynamics 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:

\mathrm{\Delta U=Q-W}

Given: Initial internal energy \mathrm{(U_{final})=1500 J}Heat added (Q) = 300 J
Work done (W) = −400 J (negative because work is done on the surroundings)
Substitute the values into the equation:

\mathrm{\begin{gathered} \Delta U=300 \mathrm{~J}-(-400 \mathrm{~J}) \\ \Delta U=300 \mathrm{~J}+400 \mathrm{~J} \\ \Delta U=700 \mathrm{~J} \end{gathered}}

The change in internal energy is 700 J. To find the final internal energy
\mathrm{U_{final}}, add the change in internal energy to the initial internal energy:

\mathrm{\begin{gathered} U_{\text {final }}=U_{\text {initial }}+\Delta U \\ U_{\text {final }}=1500 \mathrm{~J}+700 \mathrm{~J} \\ U_{\text {final }}=2200 \mathrm{~J} \end{gathered}}

Therefore, the final internal energy of the gas is 2200 J. Therefore, the correct option is C.

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