One mole of an ideal gas goes from an initial state $A$ to a final state $B$ via two processes: It first undergoes isothermal expansion from volume $V$ to $3V$ and then its volume is reduced from $3V$ to $V$ at constant pressure. The correct $P-V$ diagram representing the two processes is:

$A$ thermodynamic system is taken from an initial state $i$ with internal energy $U_i = 100 \ J$ to the final state $f$ along two different paths $iaf$ and $ibf$,as schematically shown in the figure. The work done by the system along the paths $ia$,$af$,$ib$ and $bf$ are $W_{ia} = 50 \ J$,$W_{af} = 200 \ J$,$W_{ib} = 50 \ J$ and $W_{bf} = 100 \ J$ respectively. The heat supplied to the system along the paths $iaf$ and $ibf$ are $Q_{iaf}$ and $Q_{ibf}$ respectively. If the internal energy of the system in the state $b$ is $U_b = 200 \ J$ and $Q_{iaf} = 500 \ J$,the ratio $Q_{ibf} / Q_{iaf}$ is:

Three moles of an ideal monatomic gas perform a cycle $ABCDA$ as shown in the figure. The temperatures of the gas at the states $A, B, C$ and $D$ are $400 \, K, 800 \, K, 2400 \, K$ and $1200 \, K$, respectively. The work done by the gas during this cycle is ($R$ is the universal gas constant). (in $R$)

What are the limitations of the first law of thermodynamics?

The ratio of the work done, change in internal energy, and heat absorbed when a diatomic gas expands at constant pressure is

$A$ cyclic process $ABCA$ is shown in the $V-T$ diagram. The corresponding process on the $P-V$ diagram is: