Question

The ratio of specific heats for oxygen is 1.4. Density of oxygen at STP $ =\text{ }1.44\text{ }kg/{{m}^{3}}. $ If atmospheric pressure is $ 1.013\times {{10}^{5}}N/{{m}^{2}}, $ the specific heat at constant volume is:

• 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}} $

Answer 1

Answer: (B)

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 $