Thermodynamics Question 258
Question: The pressure inside a tyre is 4 times that of atmosphere. If the tyre bursts suddenly at temperature 300 K, what will be the new temperature?
Options:
A) $ 300{{( 4 )}^{772}} $
B) $ 300{{( 4 )}^{2/7}} $
C) $ 300{{( 2 )}^{772}} $
D) $ 300{{( 4 )}^{-2/7}} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Under adiabatic change $ \frac{T _{1}}{T _{2}}{{( \frac{P _{1}}{P _{2}} )}^{\frac{1-\gamma }{\gamma }}}\text{or}T _{2}=T _{1}{{( P _{1}/P _{2} )}^{\frac{1-\gamma }{\gamma }}} $
$ \therefore T _{2}=300{{(4/1)}^{\frac{1-( 7/5 )}{( 7/5 )}}}; $
$ \gamma =1.4=7/5\text{ for air} $
$ \text{or }T _{2}=300{{( 4 )}^{-2/7}} $
