Air is contained in a frictionless piston-cylinder arrangement as shown in the figure.The atmospheric pressure is 100 kPa and the initial pressure of air in the cylinder is 105 kPa. The area of piston is 300 cm2. Heat is now added and the piston moves slowly from its initial position until it reaches the stops. The spring constant of the linear spring is 12.5 N/mm. Considering the air inside the cylinder as the system, the work interaction is ________ J. (round off to the nearest integer).Correct answer is '544'. Can you explain this answer?

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Air is contained in a frictionless piston-cylinder arrangement as shown in the figure.

The atmospheric pressure is 100 kPa and the initial pressure of air in the cylinder is 105 kPa. The area of piston is 300 cm². Heat is now added and the piston moves slowly from its initial position until it reaches the stops. The spring constant of the linear spring is 12.5 N/mm. Considering the air inside the cylinder as the system, the work interaction is ________ J. (round off to the nearest integer).

Correct answer is '544'. Can you explain this answer?

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Air is contained in a frictionless piston-cylinder arrangement as show...

P₀ = 100 kPa, P₁ = 105 kPa, K = 12.5 N/mm = 12.5 kN/m
A = 300 cm² = 300 × 10–4 m²
x = 8 cm = 8 × 10^–2 m
1-2 constant pressure
W_1-2 = P₁ × A × x = 105 × 300 × 10^–4 × 8 × 10^–2
= 0.252 kJ = 252 J
P₂ = 105 kPa

P₃ × A = P₂A + Kx

W_2-3 = 0.2919 kJ = 291.9 J
∴
W_total = W_1-2 + W_2-3 = 0.5439 kJ = 543.91 ≈ 544 J
Alternate Solution:
Total work = Workdone because of 105 kPa pressure + Workdone against spring which is equal to energy stored in spring

= 0.504 + 0.04
= 0.544 kJ = 544 J

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Air is contained in a frictionless piston-cylinder arrangement as shown in the figure.The atmospheric pressure is 100 kPa and the initial pressure of air in the cylinder is 105 kPa. The area of piston is 300 cm2. Heat is now added and the piston moves slowly from its initial position until it reaches the stops. The spring constant of the linear spring is 12.5 N/mm. Considering the air inside the cylinder as the system, the work interaction is ________ J. (round off to the nearest integer).Correct answer is '544'. Can you explain this answer?

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