One mole of an ideal gas at initial temperature $T$, undergoes a quasi-static process during which the volume $V$ is doubled. During the process, the internal energy $U$ obeys the equation $U=a V^3$, where $a$ is a constant. The work done during this process is

A cyclic process for $1\, mole$ of an ideal gas is shown in figure in the $V-T,$ diagram. The work done in $AB, BC$ and $CA$ respectively

Half mole of an ideal monoatomic gas is heated at constant pressure of $1\, atm$ from $20\,^oC$ to $90\,^oC$. Work done by has is close to ….. $J$ (Gas constant $R = 8.31\, J/mol.K$)

A thermodynamic system is taken form an initial state $i$ with internal energy $U_1=100 \ J$ to the final state along two different paths iaf and ibf, as schematically shown in the fire. The work done by the system along the paths $af$, ib and bf are $W _{ af }=200 \ J , W _{ ID }=50 \ J$ and $W _{ br }=100 \ J$ respectively. The heat supplied to the system along the path iaf, ib and bf are $Q_{\mid a t l} Q_{b r}$ and $Q_{10}$ respectively. If the internal energy of the sytem in the state $b$ is $U_b=$ $200 \ J$ and $Q_{l a t}=500 \ J$, the ratio $Q_{b J} / Q_{10}$ is:

One mole of an ideal diatomic gas undergoes a transition from $A$ to $B$ along a path $AB$ as shown in the figure. 

The change in internal energy of the gas during the transition is …………$\;kJ$