When the amount of work done is $333 \ cal$ and the change in internal energy is $167 \ cal$,then the heat supplied is ....... $cal$.

$A$ gas is compressed at a constant pressure of $50 \ N/m^{2}$ from a volume of $10 \ m^{3}$ to $4 \ m^{3}$. Then,the gas is heated by supplying $100 \ J$ of energy. The increase in its internal energy will be ..... $J$.

In a thermodynamic process,the pressure of a fixed mass of a gas is changed in such a manner that the gas releases $30 \ J$ of heat and $10 \ J$ of work is done on the gas. If the initial internal energy of the gas was $30 \ J$,then the final internal energy will be ........ $J$.

In a thermodynamic process,$200 \ J$ of heat is given to a gas and $100 \ J$ of work is also done on it. The change in internal energy of the gas is ........ $J$.

$A$ given quantity of gas is taken from $A$ to $C$ in two ways: $a$) directly from $A \rightarrow C$ along a straight line, and $b$) in two steps, from $A \rightarrow B$ and then from $B \rightarrow C$. The work done and heat absorbed along the direct path $A \rightarrow C$ are $200 \ J$ and $280 \ J$ respectively. If the work done along the path $A \rightarrow B \rightarrow C$ is $80 \ J$, find the heat absorbed along this path.

$A$ gas is at a constant pressure of $4 \times 10^5 \,N/m^2$. When a heat energy of $2000 \,J$ is supplied to the gas, its volume changes by $3 \times 10^{-3} \,m^3$. What is the increase in its internal energy (in $\,J$)?