A) \[300\text{ }{{\left( 4 \right)}^{772}}\]
B) \[300\text{ }{{\left( 4 \right)}^{2/7}}\]
C) \[300\text{ }{{\left( 2 \right)}^{772}}\]
D) \[300{{\left( 4 \right)}^{-2/7}}\]
Correct Answer: D
Solution :
[d] Under adiabatic change \[\frac{{{T}_{1}}}{{{T}_{2}}}{{\left( \frac{{{P}_{1}}}{{{P}_{2}}} \right)}^{\frac{1-\gamma }{\gamma }}}\,\,\,\,\,\,\,\,\text{or}\,\,\,\,\,\,\,\,\,\text{ }{{T}_{2}}={{T}_{1}}{{\left( {{P}_{1}}/{{P}_{2}} \right)}^{\frac{1-\gamma }{\gamma }}}\] \[\therefore {{T}_{2}}=300{{(4/1)}^{\frac{1-\left( 7/5 \right)}{\left( 7/5 \right)}}};\] \[\gamma =1.4=7/5\text{ for air}\] \[\text{or }{{T}_{2}}=300{{\left( 4 \right)}^{-2/7}}\]
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