The P-V diagram of path followed by one mole of perfect gas in a cylindrical container is shown in figure, the work done when the gas is taken from state A to state B is:

2 P_{2} V_{1} [1 - \frac{{\sqrt{V}}_{2}}{{\sqrt{V}}_{1}}

]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 P_{1} V_{1} [1 - \frac{{\sqrt{V}}_{1}}{{\sqrt{V}}_{2}}

]

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2 P_{2} V_{2} [1 - \frac{{\sqrt{V}}_{1}}{{\sqrt{V}}_{2}}

]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 P_{1} V_{2} [1 - \frac{{\sqrt{V}}_{1}}{{\sqrt{V}}_{2}}

]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $2 P_{1} V_{1} [1 - \frac{{\sqrt{V}}_{1}}{{\sqrt{V}}_{2}}$ ]
We know that in the polytropic process $P V^{n} = C$
work done from state $1$ to $2$ is

$W = \frac{P_{1} V_{2} - P_{2} V_{2}}{n - 1}$

here we have $n = \frac{1}{2}$

$\Rightarrow w = \frac{P_{1} V_{1} - P_{2} V}{\frac{1}{2} - 1} = 2 (P_{2} V_{2} - P_{1} V_{1}) = 2 P_{2} V_{2} (1 - \frac{P_{1} V_{1}}{P_{2} V_{2}})$

$∵ P V^{1 / 2} = C$

$\Rightarrow P V^{1 / 2} . V^{1 / 2} = C . V^{1 / 2}$

$\Rightarrow P V = C V^{1 / 2} \Rightarrow P_{1} V_{1} = C \sqrt{V_{1}}$

and $P_{2} V_{2} = C \sqrt{V_{2}}$

$\Rightarrow W = 2 P_{2} V_{2} (1 - \frac{C \sqrt{V_{1}}}{C \sqrt{V_{2}}}) = 2 P_{2} V_{2} (1 - \frac{\sqrt{V_{1}}}{\sqrt{V_{2}}})$

Suggest Corrections

Similar questions

Work done by a system under isothermal change from a volume $V_{1}$ to $V_{2}$ for a gas which obeys Vander Waal's equation $(V - β n) (P + \frac{α n^{2}}{V}) = n R T$

Q. Work done by a system under isothermal change from a volume

V_{1} t o V_{2}

for a gas which obeys Vander Waal's equation

(V - β n) (P + \frac{a n^{2}}{V}) = n R T

Q. Three blocks 1, 2 and 3 are arranged as shown in the figure. The velocities of the blocks

v_{1}, v_{2}

and

v_{3}

are shown in the figure. What is the relationship between

v_{1}, v_{2}

and

v_{3}

In the circuit shown in the figure, reading of voltmeter is $V_{1}$ when only $S_{1}$ is closed, $V_{2}$ when only $S_{2}$ is closed and $V_{3}$ when both $S_{1}$ and $S_{2}$ are closed. Choose the correct relation between $V_{1}$ , $V_{2}$ and $V_{3}$ .

A gas expands under constant pressure P from volume $V_{1}$ to $V_{2}$ . The work done by the gas is

Join BYJU'S Learning Program