What will be the average kinetic energy per molecule in SI units for an ideal gas at a temperature of $25^ ext{o}C$?

Question

What will be the average kinetic energy per molecule in SI units for an ideal gas at a temperature of $25^	ext{o}C$?

Accepted Answer

**Solution:**

1. Convert temperature from Celsius to Kelvin:
   $$T(K) = T(^\circ C) + 273.15 = 25 + 273.15 = 298.15 	ext{ K}$$

2. Use the formula for average kinetic energy per molecule of an ideal gas:
   $$KE_{avg} = \frac{3}{2} k_B T$$
   where $k_B = 1.38 	imes 10^{-23} 	ext{ J/K}$ (Boltzmann constant).

3. Substitute the values:
   $$KE_{avg} = \frac{3}{2} 	imes 1.38 	imes 10^{-23} 	imes 298.15$$
   $$= 1.5 	imes 1.38 	imes 10^{-23} 	imes 298.15$$

4. Calculate:
   $$1.5 	imes 1.38 = 2.07$$
   $$2.07 	imes 298.15 \approx 617.5$$
   So,
   $$KE_{avg} = 617.5 	imes 10^{-23} = 6.175 	imes 10^{-21} 	ext{ J}$$

**Answer:** The average kinetic energy per molecule is approximately $6.17 	imes 10^{-21} 	ext{ J}$.

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