Question

A gas in the initial state A having pressure ${5Nm}^{-2}$ and volume ${2m}^3$ is changed to state C having pressure ${15Nm}^{-2}$ and volume ${6m}^3$ following paths ABC and AC. Path ABC includes path AB and BC. The state B has pressure ${15Nm}^{-2}$ and volume ${2m}^3$. Calculate:
(a) Path along which work done is least.
(b) Internal energy at C, if the internal energy of gas at A is 10J and amount of heat supplied to change its state to C through the path AC is 200J.
(c) Amount of heat supplied to gas to go from A to B, if internal energy of gas at state B is 10J.
Find the value of $W_{AC}+U_C+Q_{AB}$.

Answer 1

a) Along path AC, the work done is least. Because the areas under $P-V$ diagram along AC is less as compared to along the path ABC.

$W_{ABC}=-(15\times 4)=-60J$

$W_{AC}=-(5\times 4+\frac{10\left(4\right)}{2})=-40J$

b) $W_{AC}=-40J$ from above

$△Q_{AC}=200J$
From the first law of thermodynamics-
$\Delta U=q+W=200-40=160J$

$△U_{AC}=U_C-U_A=160J$

$U_C=U_A+160=10+160=170J$

c) $△W_{AB}=0$

$△U_{AB}=U_B-U_A=10-10=0$

$△Q_{A\to B}=0$