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    "# 5.8 – Path and State functions \n",
    "\n",
    "---"
   ]
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    "## 5.8.0 – Learning Objectives\n",
    "\n",
    "By the end of this section you should be able to:\n",
    "\n",
    "1. Build further knowledge of state variable and state functions.\n",
    "2. Explain the difference between state and path functions.\n",
    "3. Classify thermodynamic terms as state or path variables. \n",
    "\n",
    "---"
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    "## 5.8.1 – Introduction\n",
    "\n",
    "State and path functions are how variables in a system change from an initial state to a final state. In this notebook, you will learn about state and path variables, state and path functions, their differences, and their uses.\n",
    "\n",
    "---"
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    "## 5.8.2 – State Functions\n",
    "Remember that guy who went up Mount Everest? Imagine you are a tourist at the bottom and see that guy on top of the mountain. __Regardless of how he got there__, that guy got there and is 8,848m higher than you are and thus he has 8679888J of potential energy more than you (assuming they weigh 100kg). \n",
    "\n",
    " A __State function__ is the change of the state of a variable __regardless of the path it takes__. __Internal Energy__ $U$, __Enthalpy__ $H$, __Pressure__ $P$, __Temperature__ $T$, and __Volume__ $V$ are state functions. \n",
    "\n",
    "But __how__ did that guy get up there? Did he skydive out of a plane? Did he climb up there himself? Was he carried up by a Sherpa? Now we are concerned about the path the guy took to get up there. \n",
    "\n",
    "A __Path function__ is the transition of __path variables__ from one state to another. __Work__ $W$ and __Heat__ $Q$ are path variables. They change depending on what path is chosen to reach a state.\n",
    "\n",
    "---"
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    "## 5.8.3 – Path functions change the amount of work done on/by a system: \n",
    "\n",
    "Let’s take a look at the diagram below:\n",
    "\n",
    "![](../figures/Module-5/state1.svg)\n",
    "\n",
    "$U1$ is at an initial state of $P_i$ and $T_i$. Our goal is to get to $U2$. Here we are presented with 2 options.\n",
    "\n",
    "\n",
    "![](../figures/Module-5/paths.svg)\n",
    "\n",
    "In **Path 1**, the system is isochorically compressed and then expanded to the state U2. In **Path 2**, the system is isobarically expanded, then isochorically compressed to the state U2. \n",
    "\n",
    "![](../figures/Module-5/workdone.svg)\n",
    "\n",
    "As Work is $P \\Delta V$,  it is clear that the work done is much greater in the first path. This is because the magnitude of volumetric expansion was executed at a higher pressure than the second path. \n",
    "\n",
    "__Furthermore:__ We can infer that there is more heat transferred to system 1 since U2 is constant for both and using the information from the first law $U = Q  - W$ , if W is larger, than Q must be larger to raise the value of U2"
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