- 2069 Poush · 5 marks
Free-moving piston between two chambers
Short answer
Masses: mA = 0.5/100 = 0.005 kg, mB = 0.5/50 = 0.010 kg. With piston at one‑fourth length, VA = 0.25 m³, VB = 0.75 m³. Final specific volumes: vA = 0.25/0.005 = 50 m³/kg, vB = 0.75/0.010 = 75 m³/kg.
The device shown in figure below has a free moving piston between the two chambers. The initial total volumes of A and B are equal with VA = 100 m³/kg and VB = 50m³/kg. If the piston is moved so that x is one-fourth of the entire length, determine the final specific volumes of chambers A and B. [Figure: a horizontal cylinder with chambers A (left) and B (right) separated by a piston; x is the distance of the piston from the left end; total volume marked 1 m³.]
Given: chambers A and B, separated by a free piston; total volume 1 m³; initially V_A = V_B (each 0.5 m³); v_A = 100 m³/kg, v_B = 50 m³/kg. Finally the piston is at x = one-fourth of the length. We assume x is measured from the A end, so V_A = ¼ of the total volume. No mass crosses the piston, so m_A and m_B remain constant.
Step 1: Masses
m_A = 0.5/100 = 0.005 kg
m_B = 0.5/50 = 0.010 kg
Step 2: Final volumes (constant cross-section, so volume ∝ length)
V_A2 = ¼ × 1 = 0.25 m³
V_B2 = ¾ × 1 = 0.75 m³
Step 3: Final specific volumes
v_A2 = V_A2/m_A = 0.25/0.005 = 50 m³/kg
v_B2 = V_B2/m_B = 0.75/0.010 = 75 m³/kg
Answer: v_A = 50 m³/kg and v_B = 75 m³/kg. (If x were measured from the B end, V_A = 0.75 m³ and V_B = 0.25 m³, giving v_A = 150 m³/kg and v_B = 25 m³/kg.)
✓ Answer checked by Claude Opus 5.5 (high effort)
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