Thermodynamics Question 269

Question: The state of an ideal gas is changed through an isothermal process at temperature $ T _{0} $ . The work done by gas in going from state B to C is double the work done by gas in going from state A to B. If the pressure in the state B is $ P _{0}/2 $ then the pressure of the gas in state C is

Options:

A) $ P _{0}/2 $

B) $ P _{0}/4 $

C) $ P _{0}/6 $

D) $ P _{0}/8 $

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Answer:

Correct Answer: D

Solution:

[d] Work done by gas in going isothermally from stated to 5 is $ \Delta W _{AB}=nRT\text{ In}\frac{P _{A}}{P _{B}}=nRT\text{ In 2} $ ….(i)

Work done by gas in going isothermally from state B to C is $ \Delta W _{BC}=nRT\text{ In}\frac{P _{B}}{P _{C}}=nRT\frac{P _{0}}{2P _{C}} $ …(ii)

It is given that $ \Delta W _{BC}=2\Delta W _{AB} $

$ \text{In }\frac{P _{0}}{2P _{C}}=\text{In}{{( \text{2} )}^{2}}\text{ }\therefore {{\text{P}} _{C}}=\frac{P _{0}}{8} $



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