The cylinder shown in the figure has conducting walls and temperature of the surrounding is T, the piston is initially in equilibrium, the cylinder contains n moles of a gas, Now the piston is displaced slowly by an external agent to make the volume double of the initial. Find work done by external agent in term of n, R, T

n moles of a gas are filled in a container at temperature T. If the gas is slowly and isothermally compressed to half its initial volume, the work done by the atmosphere on the gas is

A short electric dipole of dipole moment P is placed in stable equilibrium in uniform electric field E as shown in the figure. The work done by the external agent to rotate the dipole slowly up to its unstable equilibrium will be

A cylinder fitted with a piston contains 0.2 moles of air at temperature 27^(@) . The piston is pushed so slowly that the air within the cylinder remains in thermal equilibrium with the surroundings. Find the approximate work done by the system if the final volume is twice the initial volume

In a cylindrical container two pistons enclose gas in two compartments as shown in the figure. The pistons have negligible thickness and can move without friction. The sys- tem is originally in equilibrium. The outer piston is slowly moved out by 10 cm and the inner piston is found to move by 4 cm. Find the distance of the inner piston in equilibrium from the closed end of the cylinder if the outer piston is slowly moved out of the cylinder. Assume temperature of the gas to remain constant.

An ideal gas is enclosed in a vertical cylindrical container and supports a freely moving piston of mass M. The piston and the cylinder have an equal cross-sectional area A. Atmospheric pressure is p_(0) and when the piston is in equilibrium, the volume of the gas is V_(0) . The piston is now displaced slightly from its equilibrium position. Assuming that the system, is completely isolated from, its surroundings, what is the frequency of oscillation.

n moles of a gas fille in a a container temperature T is in thermodynamic equilibrium initially. If the gas is compressed slowly and isothermally so half its initial volume volume the work done by the atmosphere on the piston is :