The above $P-V$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

One mole of an ideal gas undergoes a cyclic process, consisting of two isochores and two isobars. Temperature at $1$ and $3$ equal to $T_1$ and $T_3$ respectively. The work done by the gas over the cycle, if the point $2$ and $4$ lie on the same isotherm

$n$ mole a perfect gas undergoes a cyclic process $ABCA$ (see figure) consisting of the following processes.

$A \rightarrow B :$ Isothermal expansion at temperature $T$ so that the volume is doubled from $V _{1}$ to $V _{2}=2 V _{1}$ and pressure changes from $P _{1}$ to $P _{2}$

$B \rightarrow C :$ Isobaric compression at pressure $P _{2}$ to initial volume $V _{1}$

$C \rightarrow A$ : Isochoric change leading to change of pressure from $P _{2}$ to $P _{1}$

Total workdone in the complete cycle $ABCA$ is

Figure shows a polytropic process for an ideal gas. The work done by the gas will be in process $AB$ is

A sample of ideal gas $(\gamma = 1.4)$ is heated at constant pressure. If an $100\, J$ is supplied to gas, the work done by the gas is …… $J$