`=>` Let us first examine a change in internal energy by doing work.
`=>` We take a system containing some quantity of water in a thermos flask or in an insulated beaker.
● This would not allow exchange of heat between the system and surroundings through its boundary and we call this type of system as `color{green}("adiabatic")`. The manner in which the state of such a system may be changed will be called `text(adiabatic process)`.
`color{green}("Adiabatic Process ")` It is a process in which there is no transfer of heat between the system and surroundings.
● Here, the wall separating the system and the surroundings is called the `color{red}("adiabatic wall")` (Fig 6.3).
`=>` Let us bring the change in the internal energy of the system by doing some work on it.
● Let us call the initial state of the system as state `A` and its temperature as `T_A`.
● Let the internal energy of the system in state `A` be called `U_A`.
● We can change the state of the system in two different ways :
`color{green}("One way" )` We do some mechanical work, say `1` `kJ`, by rotating a set of small paddles and thereby churning water. Let the new state be called `B` state and its temperature, as `T_B`.
● It is found that `T_B > T_A` and the change in temperature, `ΔT = T_B–T_A`.
● Let the internal energy of the system in state `B` be `U_B` and the change in internal energy, `ΔU =U_B– U_A.`
`color{green}("Second way ")` We now do an equal amount (i.e., `1` `kJ`) electrical work with the help of an immersion rod and note down the temperature change. We find that the change in temperature is same as in the earlier case, say, `T_B – T_A`.
`=>` In fact, the experiments in the above manner were done by J. P. Joule between `1840–50` and he was able to show that a given amount of work done on the system, no matter how it was done (irrespective of path) produced the same change of state, as measured by the change in the temperature of the system.
● So, it seems appropriate to define a quantity, the internal energy `U`, whose value is characteristic of the state of a system, whereby the adiabatic work, `w_(ad)` required to bring about a change of state is equal to the difference between the value of `U` in one state and that in another state, `ΔU` i.e.,
`ΔU = U_2 −U_1 = w_(ad)`
Therefore, internal energy, `U`, of the system is a state function.
`=>` The positive sign expresses that `w_(ad)` is positive when work is done on the system.
`=>` If the work is done by the system,`w_(ad)` will be negative.
`=>` Some of other familiar state functions are `V`, `p`, and `T`.
`color{red}("Example" )` (i) If we bring a change in temperature of the system from `25°C` to `35°C`, the change in temperature is `35°C–25°C = +10°C`, whether we go straight up to `35°C` or we cool the system for a few degrees, then take the system to the final temperature. Thus, `T` is a state function and the change in temperature is independent of the route taken.
(ii) Volume of water in a pond, for example, is a state function, because change in volume of its water is independent of the route by which water is filled in the pond, either by rain or by tubewell or by both.
`=>` Let us first examine a change in internal energy by doing work.
`=>` We take a system containing some quantity of water in a thermos flask or in an insulated beaker.
● This would not allow exchange of heat between the system and surroundings through its boundary and we call this type of system as `color{green}("adiabatic")`. The manner in which the state of such a system may be changed will be called `text(adiabatic process)`.
`color{green}("Adiabatic Process ")` It is a process in which there is no transfer of heat between the system and surroundings.
● Here, the wall separating the system and the surroundings is called the `color{red}("adiabatic wall")` (Fig 6.3).
`=>` Let us bring the change in the internal energy of the system by doing some work on it.
● Let us call the initial state of the system as state `A` and its temperature as `T_A`.
● Let the internal energy of the system in state `A` be called `U_A`.
● We can change the state of the system in two different ways :
`color{green}("One way" )` We do some mechanical work, say `1` `kJ`, by rotating a set of small paddles and thereby churning water. Let the new state be called `B` state and its temperature, as `T_B`.
● It is found that `T_B > T_A` and the change in temperature, `ΔT = T_B–T_A`.
● Let the internal energy of the system in state `B` be `U_B` and the change in internal energy, `ΔU =U_B– U_A.`
`color{green}("Second way ")` We now do an equal amount (i.e., `1` `kJ`) electrical work with the help of an immersion rod and note down the temperature change. We find that the change in temperature is same as in the earlier case, say, `T_B – T_A`.
`=>` In fact, the experiments in the above manner were done by J. P. Joule between `1840–50` and he was able to show that a given amount of work done on the system, no matter how it was done (irrespective of path) produced the same change of state, as measured by the change in the temperature of the system.
● So, it seems appropriate to define a quantity, the internal energy `U`, whose value is characteristic of the state of a system, whereby the adiabatic work, `w_(ad)` required to bring about a change of state is equal to the difference between the value of `U` in one state and that in another state, `ΔU` i.e.,
`ΔU = U_2 −U_1 = w_(ad)`
Therefore, internal energy, `U`, of the system is a state function.
`=>` The positive sign expresses that `w_(ad)` is positive when work is done on the system.
`=>` If the work is done by the system,`w_(ad)` will be negative.
`=>` Some of other familiar state functions are `V`, `p`, and `T`.
`color{red}("Example" )` (i) If we bring a change in temperature of the system from `25°C` to `35°C`, the change in temperature is `35°C–25°C = +10°C`, whether we go straight up to `35°C` or we cool the system for a few degrees, then take the system to the final temperature. Thus, `T` is a state function and the change in temperature is independent of the route taken.
(ii) Volume of water in a pond, for example, is a state function, because change in volume of its water is independent of the route by which water is filled in the pond, either by rain or by tubewell or by both.