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

Three processes compose a thermodynamics cycle shown in the $PV$ diagram. Process $1\rightarrow 2$ takes place at constant temperature. Process $2\rightarrow 3$ takes place at constant volume, and process $3\rightarrow 1$ is adiabatic. During the complete cycle, the total amount of work done is $10\,\, J$. During process $2\rightarrow 3$, the internal energy decrease by $20\,\,J$ and during process $3\rightarrow 1,$ $20\,\, J$ of work is done on the system. How much heat is added to the system during process $1\rightarrow 2\,\,?$ ...... $J$

$P-V$ diagram of $2\, g$ of $He$ gas for $A \to B$ process is shown. What is the heat given to the gas ?

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas, is

$5.6\,liter$ of helium gas at $STP$ is adiabatically compressed to $0.7\,liter$ . Taking the initial temperature to be $T_1$ , the work done in the process is

$1\, mole$ of an ideal gas at temperature $T_1$ expands according to the law $(P/V) =$ constant. Find the work done when the final temperature becomes $T_2$