A thermally insulated chamber of volume `2V_(0)` is divided by a frictionless piston of area `S` into two equal part `A` and `B`. Part `A` has an ideal gas at pressrue `P_(0)` and temperature `T_(0)` and part `B` is vacuum. A massless spring of force constant `K` is connected with the piston and the wall of the container as shown. Initially the spring is unstretched. The gas inside chamber `A` is allowed to expand. Let in equilibrium the spring be compressed by `x_(0)`. Then

A cylindrical adiabatic container of total volume 2V_(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 4T_(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 equilibrium is reached is.

A cylindrical adiabatic container of total volume 2V_(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 4T_(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 equilibrium is reached is.

A cylindrical adiabatic container of total volume 2V_(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 4T_(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 equilibrium is reached is.

In the arrangement shown in Fig. gas is thermally insulated. An ideal gas is filled in the cylinder having pressure P_(0) (gt atmospheric pressure P_(0) ). The spring of force constant K is initially unstretched. The piston of mass m and area S is frictionless. In equilibrium, the piston rises up by distance x_(0) , then

A diathermic piston divides adiabatic cylinder of volume V0 into two equal parts as shown in the figure. Both parts contain ideal monoatomic gases. The initial pressure and temperature of gas in left compartment are P0 and T0 while that in right compartment are 2P0 and 2T0. Initially the piston is kept fixed and the system is allowed to acquire a state of thermal equilibrium. The pressure in left compartment after thermal equilibrium is achieved is

A thermally insulated container is divided into two parts by a screen . In one part , the pressure and temperature are P and T for an ideal gas filled. In the second part it is vacuum. If now a small hole is created in the screen , then the temperature of the gas will

Following figure shows on adiabatic cylindrical container of volume V_(0) divided by an adiabatic smooth piston (area of cross-section = A ) in two equal parts. An ideal gas (C_(p)//C_(y)=lambda) is at pressure P_1 and temperature T_1 in left part and gas at pressure P_2 and temperature T_2 in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose x = displacement of the piston)

A thermally insulated container is divided into two parts by a screen. In one part the pressure and temperature are P and T for an ideal gas filled. In the second part it is vacuum. If now a small hole is created in the screen, then the temperature of the gas will