$110\; J$ of heat is added to a gaseous system,whose internal energy change is $40\; J$,then the amount of external work done is ........ $J$.

The internal energy of an ideal gas is given by $U = 1.5 PV$. It expands from $10 \ cm^3$ to $20 \ cm^3$ against a constant pressure of $2 \times 10^5 \ Pa$. Heat absorbed by the gas in the process is (in $J$)

$Assertion:$ The heat supplied to a system is always equal to the increase in its internal energy.
$Reason:$ When a system changes from one thermal equilibrium to another,some heat is absorbed by it.

An electric heater supplies heat to a system at a rate of $100 \text{ W}$. If the system performs work at a rate of $75 \text{ J/s}$, then the rate at which internal energy increases will be: (in $\text{ W}$)

$A$ resistance coil connected to an external battery is placed inside an adiabatic cylinder fitted with a frictionless piston and containing an ideal gas. $A$ current $i$ flows through the coil which has a resistance $R$. At what speed must the piston move upward in order that the temperature of the gas remains unchanged? Neglect atmospheric pressure.

$A$ system is taken from state $A$ to state $B$ along two different paths. The heat absorbed and work done by the system along these two paths are $Q_1, Q_2$ and $W_1, W_2$ respectively,then