Question Number 204885 by Tawa11 last updated on 29/Feb/24
The density of a gas is 1.775kgm³ at 29°c and 10⁵N/m² pressure, its specific heat capacity at constant pressure is 856J/kg/K. Determine the ratio of its specific heat at constant pressure to that at constant volume?
Answered by mahdipoor last updated on 29/Feb/24
$${for}\:{ideal}\:{gas}\:: \\ $$$${PV}={mRT}\Rightarrow{R}=\frac{{P}}{{T}}×\frac{{V}}{{m}}=\frac{{P}}{{T}\rho}\:\:\:\:\:\:\&\:\:\:\:\:{c}_{{p}} ={c}_{{v}} +{R} \\ $$$${k}=\frac{{c}_{{p}} }{{c}_{{v}} }=\mathrm{1}+\frac{{P}}{{T}\rho{c}_{{v}} }=\mathrm{1}+\frac{\mathrm{10}^{\mathrm{5}} }{\left(\mathrm{29}+\mathrm{273}\right)\left(\mathrm{1}.\mathrm{775}\right)\left(\mathrm{856}\right)} \\ $$$$=\mathrm{1}.\mathrm{218} \\ $$
Commented by Tawa11 last updated on 29/Feb/24
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}. \\ $$