1. Tardigrade
  2. Question
  3. Physics
  4. Study the following statements. I. Δ Q and Δ W are path independent. II. Δ Q-Δ W is path dependent. III. When Δ U=0, then heat supplied to the system is used up entirely by the system in doing work on the environment. Choose the correct statement.

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Q. Study the following statements.
I. $\Delta Q$ and $\Delta W$ are path independent.
II. $\Delta Q-\Delta W$ is path dependent.
III. When $\Delta U=0$, then heat supplied to the system is used up entirely by the system in doing work on the environment.
Choose the correct statement.

Thermodynamics

Solution:

Since $U$ is a state variable, $\Delta U$ depends only on the initial & final states and not on the path taken by the gas to go from one state to other.
However, $\Delta Q$ and $\Delta W$, in general depend on the path taken to go from the initial to final states.
Thus, from the first law of thermodynamics, i.e.
$\Delta Q-\Delta W=\Delta U$
It is clear that the combination $\Delta Q-\Delta W$ is however path independent.
Also, when $\Delta U=0 \Rightarrow \Delta Q=\Delta W$
Hence, heat supplied to the system is used up entirely by the system in doing work on the environment.
So, statement III is correct but I and II are incorrect.