Determine the average value of the translational kinetic energy of the molecules of an ideal gas at temperatures (a) `20.0^@ C and (b) 80.0^@ C`. What is the translational kinetic energy per mole of an ideal gas at (c)` 20.0^@ C and (d) 80.0^@ C`?

Explanation

To solve the problem of determining the average value of the translational kinetic energy of the molecules of an ideal gas at two different temperatures, we can follow these steps:

### Step 1: Understand the formula for average translational kinetic energy
The average translational kinetic energy (K) of a molecule in an ideal gas is given by the formula:
\[ K = \frac{3}{2} k T \]
where:
- \( k \) is the Boltzmann constant (\( k = 1.38 \times 10^{-23} \, \text{J/K} \))
- \( T \) is the absolute temperature in Kelvin.
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