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A cylindrical adiabatic container of total volume 2 V 0 divided into two equal parts by a conducting piston which is free to move as shown in figure. Each part containing identical gas at pressure P 0 . Initially temperature of left and right part is 4 T 0 and T 0 respectively. An external force is applied on the piston of area ' A ' to keep the piston at rest. The value of external force required when thermal equili

Options

  1. A8 5 P 0 A
  2. B2 5 P 0 A
  3. C5 6 P 0 A
  4. D6 5 P 0 A

Correct answer

D. 6 5 P 0 A

Step-by-step solution

If final temp is T P 0 V 0 4 R T 0 C v 4 T 0 - T = P 0 V 0 R T 0 C v T - T 0 4 T 0 - T 4 = T - T 0 4 T 0 - T = 4 T - 4 T 0 8 T 0 = 5 T T = 8 T 0 5 Final pressure In left P f = T f T 0 P i = 8 5 T 0 4 T 0 P 0 = 2 5 P 0 In right P f = 8 5 T 0 T 0 P 0 = 8 5 P 0 F o r c e = 8 P 0 5 - 2 P 0 5 A = 6 P 0 A 5

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