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) $1.4{{C}_{V}}-{{C}_{V}}=\frac{1.013\times {{10}^{5}}\times 1}{1.44\times 273}$ $0.4{{C}_{V}}=257.7$ ${{C}_{V}}=644.25\,\,J/kg-K$