![]() Thus there is no possible way to be work independent of the path for a given state of the system. This means the state of the system has changed. This equation is derived by simply dividing both sides of the equation for work done by the time taken. SI Unit: Watt (W) Power can also be defined in terms of force and velocity. Formula: Power Work done (J) / Time taken (s) Simplified formula: P W.D. If you change the path, you change the temperature of the system (since for an isothermal process $PV=constant$). Power is mathematically defined as the work done divided by the time taken. The above equation states that for a given temperature, work depends on initial and final volumes only along a single path. I.e., the work done is equal to the heat added to the system and is hence non-zero (since for an isothermal process heat transfer takes place so as to maintain a constant temperature) which means it is not a function of state. On completing a cycle, the internal energy returns to the original state so that $dU=0$. This can be proved by first law of thermodynamics which states that: This means it is not a function of state. i.e., when you return to the original state, the work done is not zero. The area enclosed by the curve gives the net work done over a complete cycle. As you can see the wok done along the two paths is clearly not the same. Here the area under graph gives the work done for the process. ![]() Now you return along some another path, say, path 2. The area under this graph gives the work done. Suppose at first you go along path 1 from $(P_2,V_2)$ to $(P_1,V_1)$. But when you consider a reversible cyclic process and draw a $P-V$ diagram of it, as shown below: $$W=\int_\right)$$Īt first sight one may see that the work done depends only on the initial and final states of volume and hence is path independent and is a state function. The work done is (assuming an isothermal process) Where $P$ is the pressure, $V$ is the volume, $T$ the temperature and $n$ the number of moles of gas particles. Consider the case of an ideal gas satisfying the relation
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