Thermodynamics Question 44
Question: A gas ($ \gamma =1.3) $ is enclosed in an insulated vessel fitted with insulating piston at a pressure of $ 10^{5}N/m^{2} $ . On suddenly pressing the piston the volume is reduced to half the initial volume. The final pressure of the gas is
[RPET 2002]
Options:
A) 273 K
B) 573 K
C) 373 K
D) 473 K
Show Answer
Answer:
Correct Answer: A
Solution:
$ \because \ T{{V}^{\gamma -1}}= $ constant
Therefore $ T _{1}V _{1}^{\gamma -1}=T _{2}V _{2}^{\gamma -1} $
Therefore $ T _{2}=T _{1}{{( \frac{V _{1}}{V _{2}} )}^{\gamma -1}}=T _{1}{{(4)}^{1.5-1}}=2T _{1} $
change in temperature $ =T _{2}-T _{1}=2T _{1}-T _{1}=T _{1}=273K $
