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Thermodynamics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsThermodynamics5 Marks
Question
The P-V diagram for a cyclic process is a triangle ABC drawn in order. The co-ordinates of A, B, C are $(4,1),(2,4)$ and $(2,1)$. The co-ordinates are in the order ( $\mathrm{P}-\mathrm{V}$ ). Pressure is in $\mathrm{Nm}^{-2}$ and volume is in litre. Calculate work done during the process from A to $\mathrm{B}, \mathrm{B}$ to C and C to A . Also, calculate work done in the complete cycle.
✓

Answer

The P-V diagram drawn as per the question is show in figure (adjacent).
  1. Work done during the process from A to B (expansion),
$\text{W}_{\text{AB}}=+\text{area ABKLA}$
= area of $\Delta\text{ABC}+\text{area or rectangle BCLK}$
$\text{W}_{\text{AB}}=\frac{1}{2}\text{BC}\times\text{AC}+\text{KL}\times\text{LC}$
Now, BC = KC = 4 - 1 = 3 litre
$= 3 \times 10^{-3}m^3$
$AC = 4 - 2 = 2 Nm^{-2}$
$LC = 2 - 0 = 2 Nm^{-2}$
$\therefore\text{W}_{\text{AB}}=\frac{1}{2}\times3\times10^{-3}\times2+3\times10^{-3}\times2$
$\text{W}_{\text{AB}}=9\times10^{-3}\text{J}$
  1. Work done during the process from B to C (compression) is,
$\text{W}_{\text{BC}}=-\text{area BCLK}=-\text{KL}\times\text{LC}$
$=-3\times10^{-3}\times2=-6\times10^{-3}\text{J}$
  1. Work done during the process from C to A. As there is no change in volume of the gas in this process, therefore,
$\text{W}_{\text{CA}}=0.$
Net work done in the complete cycle,
$\text{W}=\text{W}_{\text{AB}}+\text{W}_\text{BC}+\text{W}_\text{CA}$
$=9\times10^{-3}+(-6\times10^{-3})+0$
$=3\times10^{-3}\text{J}$

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