A) \[257.7\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}\]
B) \[644.3\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}\]
C) \[8.36\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}\]
D) \[901.2\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}\]
Correct Answer: B
Solution :
Given: \[\frac{{{C}_{P}}}{{{C}_{V}}}=1.4,\,\,T=273K\,\] ?(i) \[p=1.013\times {{10}^{5}}\,N/{{m}^{2}}\] \[\rho =1.44\,kg/{{m}^{3}}\] So, \[V=\frac{1}{1.44}{{m}^{3}}\] Also from Mayers formula, \[{{C}_{P}}-{{C}_{V}}=R=\frac{PV}{T}\] ?(ii) Putting the given values in Eq. (ii) and from Eq. (i) \[1.4{{C}_{V}}-{{C}_{V}}=\frac{1.013\times {{10}^{5}}\times 1}{1.44\times 273}\] \[0.4{{C}_{V}}=257.7\] \[{{C}_{V}}=644.25\,\,J/kg-K\]
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