Thermodynamics Question 348
Question: The pressure in the tyre of a car is four times the atmospheric pressure at 300 K. If this tyre suddenly bursts, its new temperature will be $ (\gamma =1.4) $
Options:
A) $ 300{{(4)}^{1.4/0.4}} $
B) $ 300{{( \frac{1}{4} )}^{-0.4/1.4}} $
C) $ 300{{(2)}^{-0.4/1.4}} $
D) $ 300{{(4)}^{-0.4/1.4}} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] For adiabatic process $ \frac{{{T}^{\gamma }}}{{{P}^{\gamma -1}}}= $ constant
Therefore $ \frac{T _{2}}{T _{1}}={{( \frac{P _{1}}{P _{2}} )}^{\frac{1-\gamma }{\gamma }}} $
Therefore $ \frac{T _{2}}{300}={{( \frac{4}{1} )}^{\frac{(1-1.4)}{1.4}}} $
Therefore $ T _{2}=300{{(4)}^{-\frac{0.4}{1.4}}} $
