$A$ thermodynamic system is changed from state $(P_1, V_1)$ to $(P_2, V_2)$ by two different processes. The quantity which will remain the same is

When $110 \ J$ of heat is supplied to a system and the change in internal energy is $40 \ J$,the work done is .......... $J$.

The latent heat of vaporization of water is $2240 \, J/g$. If the work done in the process of vaporization of $1 \, g$ is $168 \, J$,then the increase in internal energy is .... $J$.

If heat given to a system is $6 \, kcal$ and work done is $6 \, kJ$,then the change in internal energy is ....... $kJ$.

$A$ 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.

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