`2.00 mol` of a monoatomic ideal gas `(U=1.5nRT)` is enclosed in an adiabatic, fixed , vertical cylinder fitted with a smooth, light adiabatic piston.The piston is connected to a vertical spring of spring constant `200 N m^(-1)` as shown in .The area of cross section of the cylinder is `20.0 cm^(2)`. Initially, the spring is at its natural length and the temperature of the gas is is `300 K`. The atmosphere pressure is `100 KPa`. The gas is heated slowly for some time by means of an electric heater so as to move the piston up through `10 cm`. Find
(a) the work done by the gas
(b) the final temperature of the gas and
(c ) the heat supplied by the heater.

2.00 mol of a monatomic ideal gas (U=1.5nRT) is enclosed in an adiabatic, fixed , vertical cylinder fitted with a smooth, light adiabatic piston.the piston is connected to a vertical spring of spring constant 200 N m^(-1) as shown in .the area of cross section of the cylinder is 20.0 cm^(2) . initially, the spring is at its natural length and the temperature of the gas is at its natural length and the temperature of the gas is 300 K. the atmosphere pressure is 100 kPa. the gas is heated sloewly for some time by means of an electric heater so as to move the poston up through 10 cm. find (a) the work done by the gas (b) the final temperature of the gas and (c ) the heat supplied by the heater.

Method 3 of W Mass of a piston shown in Fig. is m and area of cross-section is A. Initially spring is in its natural length. Find work done by the gas.

By what fraction does the mass of a spring is 200 g at its natural lenth and the spring constant is 500 N m ^(-1)

A gas is enclosed in a cylindrical vessel fitted with a frictionless piston. The gas is slowly heated for some time. During the process, 10 J of heat is supplied and the piston is found to move out 10 cm. The area of cross-section of the cylinder =4cm^2 and the atmospheric pressure =100kPa .

A diatomic gas is enclosed in a vessel fitted with massless movable piston. Area of cross section of vessel is 1m^2 . Initial height of the piston is 1m (see the figure). The initial temperature of the gas is 300K. The temperature of the gas is increased to 400K, keeping pressure constant, calculate the new height of the piston. The piston is brought to its initial position with no heat exchange. Calculate the final temperature of the gas. You can leave answer in fraction.

The piston cylinder arrangement shown contains a diatomic gas at temperature 300 K The cross sectinal area of the cylinder is 1m2. Initially the height of the piston above th base of the cyclinder is 1 m. The temperature is now raised to 400 K at constant pressure. There is no heat loss in the process.. Find the new height (in m) of the piston above the base of the cylinder.

A fixed container is fitted with a piston which is attached to a spring of spring constant k . The other and of the spring is attached to a rigid wall. Initially the spring is in its natural length and the length of container between the piston and its side wall is L . Now an dideal diatomic gas is slowly filled in the container so that the piston moves quasistatically. It pushed the piston by x so that the spring now is compressed by x . The total rotaional kinetic energy of the gas molecules in terms of the displacement x of the piston is (there is vacuum outside the container)

An ideal gas enclosed in a cylinder fitted with a frictionless and weightless piston, pushes it outside. What would be the sign convention for the work ?