$A$ system is given $300$ calories of heat and it does $600$ joules of work. How much does the internal energy of the system change in this process? $(J = 4.18 \text{ Joules/cal})$ (in joule)

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 ..... $J$.

Density of water at $4 ^\circ C$ and $20 ^\circ C$ are $1000 \ kg/m^3$ and $998 \ kg/m^3$ respectively. The increase in internal energy of $4 \ kg$ water when it is heated from $4 ^\circ C$ to $20 ^\circ C$ is . . . . . . $J$. (Specific heat capacity of water $= 4.2 \ kJ/kg \cdot K$ and $1$ atmospheric pressure $= 10^5 \ Pa$)

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

The volume of a gas at a constant pressure of $50\,N/m^2$ changes from $10\,m^3$ to $4\,m^3$. If $100\,J$ of heat is supplied to the gas,the increase in internal energy is ....... $J$.

An electric heater supplies heat to a system at a rate of $100\;W.$ If the system performs work at a rate of $75\;J/s,$ at what rate (in $J/s$) is the internal energy increasing?