Answer to Question #121611 in Molecular Physics | Thermodynamics for Gopaul Yesuah

Question

A certain perfect gas is heated at constant pressure from 15 degrees celcius to 95 degrees celcius, the energy required is 1136 KJ / kg.
When this same gas is heated at constant volume to the same temperatures, the energy required is 808
KJ / kg.
Calculate:
(i) Mass heat at constant pressure, cp
(ii) Mass heat at constant volume, CV
(iii) The value of γ
(iv) The particular gas constant, Rp
(v) Molar mass, Mr

Answer 1

Solution.

$T_1=15^oC;$

$T_2=95^oC;$

$\Delta Q_1=1136KJ/kg;$

$\Delta Q_2=808KJ/kg;$

$\Delta Q_1=c_p\Delta T\implies c_p=\dfrac{\Delta Q_1}{\Delta T};$

i)$c_p=\dfrac{1136KJ/kg}{80^oC}=14.2KJ/(kg^oC);$

$\Delta Q_2=c_v\Delta T\implies c_v=\dfrac{\Delta Q_2}{\Delta T};$

ii)$c_v=\dfrac{808KJ/kg}{80^oC}=10.1KJ/(kg^oC);$

iii)$\gamma=\dfrac{c_p}{c_v};$

$\gamma=\dfrac{14.2}{10.1}=1.4;$

vi)$R_m=c_p-c_v;$

$R_m=14.2-10.1=4.1KJ/(kg^oC)$ ;

v)$R=R_mM\implies M=\dfrac{R}{R_m};$

$M=\dfrac{8.31}{4100}=0.002kg/mol;$

The gas is hydrogen (H2).

Answer: i)$c_p=14.2KJ/(kg^oC);$

ii)$c_v=10.1KJ/(kg^oC);$

iii)$\gamma =1.4;$

iv)$R_m=4.1KJ/(kg^oC);$

v)$M=0.002kg/mol.$