A) 246.1K
B) 250 K
C) 290K
D) 248 K
Correct Answer: A
Solution :
Key Idea: Adiabatic process takes place very rapidly. When a system undergoes a change under condition, that no exchange of heat takes place between the system and surroundings, then such a process is called adiabatic. \[\frac{{{p}^{\,\,\gamma -1}}}{{{T}^{\,\gamma }}}=\] constant \[\gamma \] is ratio of specific heats, P is pressure and T is temperature. \[\therefore \] \[{{\left( \frac{{{P}_{2}}}{{{P}_{1}}} \right)}^{\gamma -1}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{\gamma }}\] \[{{\left( \frac{1}{2} \right)}^{0.4}}={{\left( \frac{{{T}_{2}}}{300} \right)}^{1.4}}\] \[\therefore \] \[0.4\,[\log 1-\log 2]=1.4\,[\log {{T}_{2}}-\log \,300]\] \[\Rightarrow \] \[{{T}_{2}}=246.1\].
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