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                                    The speed of sound in hydrogen at `0^@c` is `1280 m s^(-1)`. The density of hydrogen at STP is `0.089 kg m^(-3)`. Calculate the molar heat capacities `(C_p and C_v)` of hydrogen. | 
                            
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Answer» `V=1280 m//s`, `T=0^@C=273^@K` Density of `H_2 = 0.089 kg//m^3`, `R=8.3 J//mol-K` At STP, `P=10^5 Pa`, we know `V_(sound)= sqrt((gammap)/(rho))` `1280= sqrt((gamma xx 10 ^5)/(0.089))` or ` gamma= (1280 xx 1280 xx 0.089)/10^5` `=1.48` `C_p/C_v = gamma` or `C_p - C_v =R` `C_v = (R)/(gamma-1) = (8.31)/(1.48-1)` `=18.0 J//mol-k` `C_p = gammaC_v=1.48 xx 18.0` `=26.3//mol-K`.  | 
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