State the First Law of Thermodynamics and definitions for an ideal gas.

Here are the solutions to the questions:

1. (a) i. Starting with the first law of thermodynamic show that for polyatomic gases $\gamma = \frac{C_p}{C_v} = 1.33$

Step 1: State the First Law of Thermodynamics and definitions for an ideal gas.
The First Law of Thermodynamics states that the change in internal energy $\Delta U$ of a system is equal to the heat added to the system $Q$ minus the work done by the system $W$:

$$\Delta U = Q - W$$

For an ideal gas, the internal energy depends only on temperature, and for a small change in temperature $dT$, the change in internal energy is given by:

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