During the melting of a slab of ice at $273 \ K$ at atmospheric pressure,

$A$ gas can be taken from $A$ to $B$ via two different processes $ACB$ and $ADB$. When path $ACB$ is used,$60 \, J$ of heat flows into the system and $30 \, J$ of work is done by the system. If path $ADB$ is used,the work done by the system is $10 \, J$. The heat flow into the system in path $ADB$ is ..... $J$.

Given below are two statements. One is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$ : If $dQ$ and $dW$ represent the heat supplied to the system and the work done on the system respectively,then according to the first law of thermodynamics $dQ = dU - dW$.
Reason $R$ : The first law of thermodynamics is based on the law of conservation of energy.
In the light of the above statements,choose the correct answer from the options given below:

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

$A$ container contains $1 \text{ mole}$ of a gas with molar mass $M$ and adiabatic index $\gamma = C_P/C_V$. The container is moving with a velocity $v$. When it suddenly stops,the kinetic energy of the container is converted into the internal energy of the gas. The rise in the temperature of the gas is:

If the amount of heat given to a system is $35 \ J$ and the amount of work done by the system is $-15 \ J$,then the change in the internal energy of the system is .... $J$.