One mole of a diatomic ideal gas undergoes a process shown in $P-V$ diagram. The total heat given to the gas $(\ln 2 = 0.7)$ is (in $P_0 V_0$)

Choose the incorrect statement from the following:
$S1$: The efficiency of a heat engine can be $1$,but the coefficient of performance of a refrigerator can never be infinity.
$S2$: The first law of thermodynamics is basically the principle of conservation of energy.
$S3$: The second law of thermodynamics does not allow several phenomena consistent with the first law.
$S4$: $A$ process,whose sole result is the transfer of heat from a colder to a hotter object,is impossible.

When a system is taken from a state $i$ to $f$ along the path $iaf$ (as shown in the figure),$Q = 50 \, cal$ and $W = 20 \, cal$. Along path $ibf$,$Q = 36 \, cal$.
$(i)$ What is $W$ along path $ibf$?
$(ii)$ If $W = -13 \, cal$ for path $fi$,what is $Q$ for the path $fi$?
$(iii)$ Take $E_{int,i} = 10 \, cal$,then what is $E_{int,f}$?

Heat is supplied to a diatomic gas at constant pressure. The ratio of $\Delta Q : \Delta U : \Delta W$ is

An ideal gas is taken from state $1$ to state $2$ through optional paths $A, B, C$ and $D$ as shown in the $P-V$ diagram. Let $Q, W$ and $\Delta U$ represent the heat supplied,work done,and change in internal energy of the gas,respectively. Then:

$A$ cyclic process for $1 \, \text{mole}$ of an ideal gas is shown in the $V-T$ diagram. Find the work done in processes $AB$, $BC$, and $CA$ respectively.