A thermodynamic system is taken from an initial state with internal energy $U_{\mathrm{i}}=100 \mathrm{J}$ 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 $af$ $,ib$ and $bf$ are $W_{\mathrm{af}}=200 \mathrm{J},W_{\mathrm{ib}}=50 \mathrm{J}$ and $W_{\mathrm{bf}}=100 \mathrm{J}$ respectively. The heat supplied to the system along the path $iaf\text{,} ib$ and $bf$ are $Q_{\mathrm{iaf}}, Q_{\mathrm{ib}}$ and $Q_{\mathrm{bf}}$ respectively. If the internal energy of the system in the state $b$ is $U_{\mathrm{b}}=200 \mathrm{J}$ and $Q_{\mathrm{iaf} }=500 \mathrm{J}$, then the ratio $\frac{Q_{\mathrm{bf}}}{Q_{\mathrm{ib}}}$ is

One mole of diatomic ideal gas undergoes a cyclic process $ABC$ as shown in figure. The process $BC$ is adiabatic. The temperature at $A, B$ and $C$ are $400 \mathrm{K}$, $800 \mathrm{K}$ and $600 \mathrm{K}$ respectively. Choose the correct statement.

One mole of monoatomic ideal gas is taken along two cyclic processes $E\to F\to G\to E$ and $E\to F\to H\to E$ as shown in the $p-V$ diagram.

The processes involved are purely isochoric, isobaric, isothermal or adiabatic.

Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists. 

The shown $p-V$ diagram represents the thermodynamic cycle of an engine, operating with an ideal mono atomic gas. The amount of heat, extracted from the source in a single cycle is

An ideal gas is taken around $PQRP$ as shown in the figure of $pV$ diagram. The work done during a cycle is

A graph of pressure versus volume for an ideal gas for different processes is as shown. In the graph, curve $OC$ represents