ThermodynamicsHard
Question
In the following $p - V$ diagram the equation of state along the curved path is given by $(V - 2)^{2} = 4ap$ where $a$ is a constant. The total work done in the closed path is
Options
A.$- \frac{1}{a}$
B.$+ \frac{1}{3a}$
C.$\frac{1}{2a}$
D.$- \frac{1}{3a}$
Solution
$W =$ Area of parabola
$$\begin{matrix} & \ = \frac{2}{3}(\text{~}\text{Area of rectangle}\text{~}AC31\text{ }A) \\ & \ = \frac{2}{3}P_{0}(3 - 1) = \frac{4P_{0}}{3} \end{matrix}$$
When $V = 1$
$$\begin{matrix} & \ (1 - 2)^{2} = 4{aP}_{0} \\ & P_{0} = \frac{1}{4a} \\ & \text{ }W = \frac{4}{3}P_{0} = \frac{4}{3}\frac{1}{4a} = \frac{1}{3a} \\ & {\text{ }W}_{\text{gas~}} = \frac{- 1}{3a} \end{matrix}$$
Create a free account to view solution
View Solution FreeMore Thermodynamics Questions
A cylinder of radius R made of a material of material of thermal conductivity K2 is surrounded by cylindrical shell of i...The value of internal energy in an adiabatic process :-...From the following statements concerning ideal gas at any given temperature T, select the correct one (s)...A black body has maximum wavelength λm at 2000 K. Its corresponding wavelength at 3000 K is:...A quantity of heat requirad to change the unit mass of a solid substance to its liquid state, while the temperature rema...