The compressive force in the connecting rod at equilibrium is : (A) 2000 N (B) 4000 N

Question

Two fixed and horizontal cylinders A and B having pistons (both massless) of cross sectional area 100 cm2 and 200 cm2 respectively, are connected by massless rod. The piston can move freely without friction. The cylinder A contains 100 gms of an ideal gas ( γ = 1.5) at pressure 105N/m2 and temperature T0 . The cylinder B contains identical gas at same temperature T0 but has different mass. The piston are held at the state such that volume of gas in cylinder A and cylinder B are same and is equal to 10–2m3 . The walls and piston of cylinder A are thermally insulated where as gas in cylinder B is maintained at constant temperature T0 . The whole system is in vacuum. Now the pistons are slowly released and they move towards left and mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes 25 × 10–4 m3.

The compressive force in the connecting rod at equilibrium is :

(A) 2000 N

(B) 4000 N

(C) 8000 N

(D) 10000 N

Answer 1

Correct option (C) 8000 N

Explanation:

Let the initial temperature, pressure and volume of gas in 'A' be T0 ,P0 , V0 and the area of the position A and B be a, 2a.

and B be a, 2a. Now gas in chamber ‘A’ undergoes adiabatic compression whereas gas in chamber ‘B’ undergoes isothermal expansion. Now solving for gas in 'A'

Now comparing the ***** of gas in A and B