An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $PV^n = $ constant, then $n$ is given by (Here $C_P$ and $C_V$ are molar specific heat at constant pressure and constant volume, respectively)
$n = \frac{{C - {C_V}}}{{C - {C_P}}}$
$n = \frac{{{C_P}}}{{{C_V}}}$
$n = \frac{{C - {C_P}}}{{C - {C_V}}}$
$n = \frac{{{C_P} - C}}{{C - {C_V}}}$
The internal energy change in a system that has absorbed $2\,\, kcal$ of heat and done $500\, J$ of work is ........... $\mathrm{J}$
$P-V$ diagram of an ideal gas is as shown. Find work done by the gas in $ABCD$ process
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
Given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths, $A,B,C.$ Let $Q,W$ and $U$ represent the heat supplied to, the work done by gas and the internal energy of the gas, respectively. Then which of the following conditions is true?
For free expansion of a gas, which is true