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 $
Show Answer
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\ln\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}}{2^{2}\cdot 2} $
BETA
