$A$ system goes from $A$ to $B$ via two processes $I$ and $II$ as shown in the figure. If $\Delta U_1$ and $\Delta U_2$ are the changes in internal energies in the processes $I$ and $II$ respectively, then the relation between $\Delta U_1$ and $\Delta U_2$ is

$A$ gas is compressed at a constant pressure of $50 \,N/m^2$ from a volume of $10 \,m^3$ to a volume of $4 \,m^3$. Energy of $100 \,J$ is then added to the gas by heating. Its internal energy is

$A$ sample of an ideal gas is taken through a cycle as shown in the figure. It absorbs $50 \ J$ of energy during the process $AB$,no heat during $BC$,and rejects $70 \ J$ during $CA$. $40 \ J$ of work is done on the gas during $BC$. If the internal energy of the gas at $A$ is $1500 \ J$,the internal energy at $C$ would be ........ $J$.

Describe an experiment of Benjamin Thomson regarding the heat produced by work.

$A$ resistance coil connected to an external battery is placed inside an adiabatic cylinder fitted with a frictionless piston and containing an ideal gas. $A$ current $i$ flows through the coil which has a resistance $R$. At what speed must the piston move upward in order that the temperature of the gas remains unchanged? Neglect atmospheric pressure.

If the heat given to a system is $35 \ J$ and the work done on the system is $15 \ J$,then the change in the internal energy of the system is ... $J$?