The below P-V diagram represents the thermodynamic cycle for one mole of an ideal monoatomic gas. The amount of heat, absorbed in a single cycle is `((7x)/2)P_(0)V_(0)`. The value of `X` is

The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is

The following are the P-V diagrams for cyclic processes for a gas. In which of these processes is heat absorbed by the gas?

A mixture of n_(1) moles of monoatomic gas and n_(2) moles of diatomic gas has (C_(p))/(C_(V))=gamma=1.5

In Fig., a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. the lower compartment of the container is filled with 2 moles of an ideal monoatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. the heat capacities per mole of an ideal monoatomic gas are C_(upsilon) = (3)/(2) R and C_(P) = (5)/(2) R , and those for an ideal diatomic gas are C_(upsilone) = (5)/(2) R and C_(P) = (7)/(2) R. Consider the partition to be rigidly fixed so that it does not move. when equilibrium is achieved, the final temperature of the gases will be

In Fig., a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. the lower compartment of the container is filled with 2 moles of an ideal monoatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. the heat capacities per mole of an ideal monoatomic gas are C_(upsilon) = (3)/(2) R and C_(P) = (5)/(2) R , and those for an ideal diatomic gas are C_(upsilone) = (5)/(2) R and C_(P) = (7)/(2) R. Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. the total work done by the gases till the time they achieve equilibrium will be

An ideal gas undergoes cyclic process ABCDA as shown in given P - V diagram. The amount of work done by the gas is ___

A small spherical monoatomic ideal gas bubble (gamma= (5)/(3)) is trapped inside a liquid of density rho_(l) (see figure) . Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T_(0) , the height of the liquid is H and the atmospheric pressure is P_(0) (Neglect surface tension). When the gas bubble is at a height y from the bottom , its temperature is :-

The rectangular box shown in Fig has partition which can slide without friction along the length of the box. Initially each of the two chambers of the box has one mole of a mono-atomic ideal gas (lambda=5//3) at a pressure P_0 , volume V_0 and temperature T_0 . The chamber on the left is slowly heated by an electric heater. The walls of the box and the lead wires of the heater is negligible. The gas in the left chamber expands pushing the partition until the final pressure in both chambers becomes 243P_0//32 . Determine (i) the final temperature of the gas in each chamber and (ii) the work done by the gas in the right chamber.

One mole of an ideal monoatomic gas at temperature T_0 expands slowly according to the law p/V = constant. If the final temperature is 2T_0 , heat supplied to the gas is

One mole of a monoatomic ideal gas occupies two champers of a cylinder partioned by means of a movable pision. The walls of the cylinder as well as the piston are thermal insulators. Initially equal amounts of gas fill both the chambers at ( P_(0), V_(0), T_(0) ). A coil is burnt in the left chamber which absorbs heat and expands , pushing the piston to the right . The gas on the right chamber is compressed until to pressure becomes 32 P_(0) . The work done on the gas in the right chamber is