If the specific heat capacity of air at constant pressure is 993 J kg ^(-1) K ^(-1)calculate specific heat capacity at constant volume ? Density of air at N.T.P. is 1.293 Kg //m ^(3). [E.Q.)

If the specific heat capacity of air at constant pressure is 993 J kg

1.	If the specific heat capacity of air at constant pressure is 993 J kg ^(-1) K ^(-1)calculate specific heat capacity at constant volume ? Density of air at N.T.P. is 1.293 Kg //m ^(3). [E.Q.)
Answer» Solution :Specific heat of air at constatn pressure `= C _(p) = 993 j KG ^(-1) K^(-1)` From the unit of we can SEE that the mass in kg. So the equation to be used in `C_(p) - C _(V) = r ` `PV = rT, r = (PV)/(T)` Nrmal temperature `= T = 273 K` Normal pressure `= P =1` atmosphere `= 101325 Nm ^(-2)` Volume of air `= V = ?` Mass of air `= m = 1 kg` Density of air `= p = 1. 293 kg//m ^(3)` `thereforeV = (m)/(p) = (1)/(1.293) m ^(3)` `THEREFORE r = (PV)/(T) = ( 101325)/(273) xx (1)/(1.293) = 287.04 J kg ^(-1) K ^(-1)` `therefore C _(V) = C _(p) -r = 993 - 287.04 = 705.96JKg ^(-1) K ^(-1)`