The internal energy of a monatomic ideal gas in a 20 liter cylinder is 600 J. Find the gas pressure.

1) Let us write the Mendeleev – Clapeyron equation for an ideal gas:
pV = (m / M) RT.
Let us write the equation for the internal energy of an ideal monatomic gas:
U = (3/2) (m / M) RT.

Let us express (m / M) RT from both equations:
1) (m / M) RT = (2/3) U.
2) (m / M) RT = pV.

pV = (2/3) U;
p = (2/3) U / V.

Let’s convert liters to cubic meters:
1 l. = 1 dm³ = 0.001 m³;
20 l. = 0.02 m³;

Let’s calculate the gas pressure:
p = (2/3) × 600 / 0.02 J / m³;
p = 20,000 (N ∙ m) / m³;
p = 2 ∙ 10³ N / m²;
p = 2 ∙ 10³ Pa.

Answer: Gas pressure 2 ∙ 10³ Pa or 2 kPa.




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