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11.Thermodynamics
medium
A gas is suddenly compressed to $1/4$ th of its original volume at normal temperature. The increase in its temperature is ....... $K$ $(\gamma = 1.5)$
A
$273 $
B
$573 $
C
$373 $
D
$473 $
Solution
(a) $\because \;T{V^{\gamma – 1}} = $constant $⇒$ ${T_1}V_1^{\gamma – 1} = {T_2}V_2^{\gamma – 1}$
$⇒$ ${T_2} = {T_1}{\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^{\gamma – 1}} = {T_1}{(4)^{1.5 – 1}} = 2{T_1}$
change in temperature
$ = {T_2} – {T_1} = 2{T_1} – {T_1} = {T_1} = 273\,K$
Standard 11
Physics
