Which of the following are not path functions?
I. H - T S
II. W
III. q
IV. q + W
In thermodynamics, a path function is a quantity that depends on the specific process or path taken to get from one state to another. On the other hand, state functions are independent of the path and depend only on the initial and final states.
I. \( H - T S \)
This expression represents the Gibbs free energy (\( G = H - T S \)). Since the Gibbs free energy is a state function, it depends only on the initial and final states, not on the path taken. Therefore, \( H - T S \) is a state function and not a path function.
II. W (Work)
Work (\( W \)) is a path function because it depends on the specific process or path taken to change the system's state. It is not determined solely by the initial and final states of the system.
III. q (Heat)
Heat (\( q \)) is also a path function because it depends on the specific process through which energy is transferred to or from the system. The amount of heat exchanged can vary depending on the path taken, even if the initial and final states are the same.
IV. \( q + W \) (Total energy transfer)
The sum of heat (\( q \)) and work (\( W \)) is the total energy transfer in a process. Since both heat and work are path functions, their sum, \( q + W \), is also a path function. It depends on the process used, not just the initial and final states.
The expressions that are not path functions are:
The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$, then the value of $\alpha$ is ____
A solid cylinder of mass 2 kg and radius 0.2 m is rotating about its own axis without friction with angular velocity 5 rad/s. A particle of mass 1 kg moving with a velocity of 5 m/s strikes the cylinder and sticks to it as shown in figure.
The angular velocity of the system after the particle sticks to it will be: