The internal energy change in a system that has absorbed $2 \; kcal$ of heat and done $500 \; J$ of work is ...... $J$.

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

$A$ 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.

First law of thermodynamics is represented by

The change in the internal energy of a mass of gas,when the volume changes from $V$ to $2V$ at constant pressure $P$,is (where $\gamma$ is the ratio of specific heat of gas at constant pressure to specific heat at constant volume):

$A$ 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)