Question

A certain perfect gas is compressed reversible from 1bar, 17°c to a pressure of 5bar in a perfect thermally insulated cylinder, the final temperature being 77°c
The work done on the gas during the compression is 45kj/kg
Calculate CV, R and the molecular weight of the gas

Answer 1

Solution.

$p_1=1bar;$

$p_2=5bar;$

$T_1=290K;$

$T_2=350K;$

$\dfrac{W}{m}=45000J/kg;$

$W=mC_V(T_2-T_1)\implies C_V=\dfrac{W}{m(T_2-T_1)};$ =\dfrac{W}{

$C_V=\dfrac{45000J/kg}{60K}=750J/(kg\sdot K);$

$\dfrac{T_2}{T_1}=(\dfrac{p_2}{P_1})^{\dfrac{\gamma-1}{\gamma}};$

$\dfrac{350}{290}=5^{\dfrac{\gamma-1}{\gamma}};$ $1.2=5^{\dfrac{\gamma-1}{\gamma}};\dfrac{\gamma-1}{\gamma}=0.115; \gamma=1.3;$

$R=\dfrac{R_0}{M}\implies M=\dfrac{R_0}{R};$

$C_V=\dfrac{R}{\gamma-1}\implies R=C_V(\gamma-1);$

$R=750J/(kg\sdot K)(1.3-1)=225J/(kg\sdot K);$

$M=\dfrac{8.31}{225}=37\sdot10^{-3}kg/mol;$

Answer:$C_V=750J/(kg\sdot K);$

$R=225J/(kg\sdot K)$ ;

$M=37\sdot10^{-3}kg/mol$ .