$5.6$ liter of helium gas at $STP$ is adiabatically compressed to $0.7$ liter. Taking the initial temperature to be $T_1$, the work done in the process is
$\frac{9}{8}\,R{T_1}$
$\frac{3}{2}\,R{T_1}$
$\frac{15}{8}\,R{T_1}$
$\frac{9}{2}\,R{T_1}$
A perfect gas is found to obey the relation $PV^{3/2} =$ constant, during an adiabatic process. If such a gas, initially at a temperature $T$, is compressed adiabatically to half its initial volume, then its final temperature will be
When a system is taken from state $i$ to state $f$ along the path $iaf,$ it is found that $Q = 50\, cal$ and $W = 20\, cal$. Along the path ibf $Q = 36\, cal$. Work done along the path $ibf$ will be ........... $\mathrm{cal}$
In the following indicator diagram, the net amount of work done will be
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 gas, work done by the gas, and the internal energy of the gas, respectiely, then which of the following conditions is true?