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_(a)`). 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 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

An ideal monatomic gas is confined in a cylinder by a spring-loaded piston of cross-section 8.0xx10^-3m^2 . Initially the gas is at 300K and occupies a volume of 2.4xx10^-3m^3 and the spring is in its relaxed (unstretched, unompressed) state, fig. The gas is heated by a small electric heater until the piston moves out slowly by 0.1m. Calculate the final temperature of the gas and the heat supplied (in joules) by the heater. The force constant of the spring is 8000 N//m , atmospheric pressure is 1.0xx10^5 Nm^-2 . The cylinder and the piston are thermally insulated. The piston is massless and there is no friction between the piston and the cylinder. Neglect heat loss through lead wires of the heater. The heat capacity of the heater coil is negligible. Assume the spring to be massless.

In the cylinder shown in the figure, air is enclosed under the piston. Piston mass M=60 kg, crosssectional area of the cylinder S_(0)=20 cm^(2) atmospheric pressure P_(0)=10^(5) pa alpha=37^(@) . The air temperature is constant, the friction is negligible. What is the mass of the goods that must be put on the piston so that the volume of the gas becomes half?

A fixed thermally conducting cylinder has a radius R and height L_0 . The cylinder is open at ita bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is P_0 . While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is

An ideal monatonic gas is confined in a cylinder by a spring-loaded piston of cross section 8.0xx10^(-3) m^(2). initially the gas is at 300K and occupies a volume of 2.4xx10^(-3)m^(-3) and the sprinng is in its relaxed state. The gas is heated by a small heater until the piston moves out slowly by 0.1m. Calculate the final tenoerature of the gas. The force constant if the spring is 8000Nm^(-1) ,and the atmospheric pressure is 1.0xx10^(5)Nm^(-2).Hte cylinder and the piston are thermally insylated. The piston and the spring are massless and there is no friction between the piston and the cylinder. Neglect any heat-loss through the lead wires of the heater. The heat capacity of the heater coil is negligible.

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T_1 , pressure P_1 and volume V_1 and the spring is in its relaxed state. The gas is tehn heated very slowly to temperature T_2 ,pressure P_2 and volume V_2 . During this process the piston moves out by a distance x. Ignoring the friction between the piston and the cylinder, the correct statement (s) is (are)

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.

A weightless piston divides a thermally insulated cylinder into two parts of volumes V and 3V.2 moles of an ideal gas at pressure P = 2 atmosphere are confined to the part with volume V =1 litre. The remainder of the cylinder is evacuated. The piston is now released and the gas expands to fill the entire space of the cylinder. The piston is then pressed back to the initial position. Find the increase of internal energy in the process and final temperature of the gas. The ratio of the specific heats of the gas, gamma =1.5 .