An ideal gas is contained in a thermally insulated rigid container. It is heated by a filament of $100 \, \Omega$ resistance by passing a current of $1 \, A$ for $5 \, \text{min}$. The change in internal energy is .... $kJ$?

The first law of thermodynamics is a special case of:

$A$ 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 ........ $J$.

Heat given to a system is $35 \ J$ and work done by the system is $15 \ J$. The change in the internal energy of the system will be ..... $J$.

$A$ thermally insulated rigid container of $1 \,L$ volume contains a diatomic ideal gas at room temperature. $A$ small paddle installed inside the container is rotated from the outside,such that the pressure rises by $10^{5} \,Pa$. The change in internal energy is close to ............... $J$.

In a thermodynamic process,the pressure of a fixed mass of a gas is changed in such a manner that the gas molecules release $20 \ J$ of heat and $10 \ J$ of work is done on the gas. If the initial internal energy of the gas was $40 \ J$,then the final internal energy will be ........ $J$.