Question

The given figure shows a change of state A to state C by two paths ABC and AC for an ideal gas. Calculate the:
(1) Amount of heat supplied (in J) to the gas to go from A to B if the internal energy of a gas at state B is 20 J.

Answer 1

For the path ABC, $=W_{AB}+W_{BC}$
$=AreaunderP-Vcurve$
$=AreacoveredbylineAB+AreaofsquarebelowlineBC$
$0-15\times 4$
$=-60J$
For the path AC,$W_{AC}$=Area occupied below line AC
$W_{AC}=-\left[\frac{1}{2}\right(5+15)\times (6-2\left)\right]$
$=-40J$
The work done along AC is least.
$q=\Delta U-w$
or $\Delta U=q+\left(w\right)=200+(-40)=160J$

or $U_C-U_A=160J$
${\therefore U}_C=160+10=170J(\because U_A=10J)$
$q=\Delta U-w(w=0)$
$q=\Delta U=U_B-U_A=20-10=10J$