When a system is taken from state $a$ to state $c$ along a path $abc$,it is found that $Q = 80 \ cal$ and $W = 35 \ cal$. Along path $adc$,$Q = 65 \ cal$. The work done $W$ along path $adc$ is: (in $cal$)

$A$ gas is expanded from an initial state to a final state along a path that consists of $(a)$ an isothermal expansion doing $40 \,J$ work,$(b)$ an adiabatic expansion doing $W$ work,$(c)$ an isothermal expansion doing $30 \,J$ work. If the total change in the internal energy of the gas is $-20 \,J$,the work done by the gas during the adiabatic expansion $W=$ (in $\,J$)

Which of the following is not a thermodynamic state function?

$1 \, kg$ of a gas does $20 \, kJ$ of work and receives $16 \, kJ$ of heat when it is expanded between two states. $A$ second kind of expansion can be found between the initial and final states which requires a heat input of $9 \, kJ$. The work done by the gas in the second expansion is ....... $kJ$.

$A$ 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.

Three moles of a gas at a temperature $T$ is heated to thrice its volume by keeping the pressure constant. If $\gamma$ is the ratio of specific heats,then the increase in internal energy of the gas is