Thirty-six grams of air in a piston-cylinder assembly undergo a Stirling cycle with a compression ratio of 7.5. At the beginning of the isothermal compression, the pressure and volume are 1 bar and 0.03 m3, respectively. The temperature during the isothermal expansion is 1200 K. Assuming the ideal gas model and ignoring kinetic and potential energy effects, determine the net work, in kJ.

Question

Engineering

Moyer

Today, 03:13

Thirty-six grams of air in a piston-cylinder assembly undergo a Stirling cycle with a compression ratio of 7.5. At the beginning of the isothermal compression, the pressure and volume are 1 bar and 0.03 m3, respectively. The temperature during the isothermal expansion is 1200 K. Assuming the ideal gas model and ignoring kinetic and potential energy effects, determine the net work, in kJ.

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Princess Beasley · Answer 1

W = 6044.709 J

Explanation:

Given

Mass of air: m = 36.00 g

P₁/P₂ = 7.5

P₁ = 1 bar = 1 bar = 10⁵ Pa

V₁ = 0.03 m³

T = 1200 K

R = 8.314472 J / (mol*K)

W = ?

We have the get n (number of moles) as follows:

P*V = n*R*T ⇒ n = P₁*V₁ / (R*T₁)

⇒ n = (10⁵ Pa) * (0.03 m³) / (8.314472 J / (mol*K) * 1200 K)

⇒ n = 0.3 mol

Then, we apply the equation

W = n*R*T₁*Ln (P₁/P₂)

⇒ W = (0.3 mol) * (8.314472 J / (mol*K)) * (1200 K) * Ln (7.5)

⇒ W = 6044.709 J