Answer to Question #297541 in Molecular Physics | Thermodynamics for Tobias Felix

Question

For a certain gas, R = 0.277 kJ/kg-K and k = 1.384. a) What are the value of cp

and cv? b) What mass of this gas will occupy a volume of 0.425 m3 at 517.11

kPaa and 26.7 0C? c) If 31.65 kJ are transferred to this gas at constant

volume, what are the resulting temperature and pressure?

Answer 1

We know that

$$n=\frac{PV}{RT}=\frac{517.11\times0.425}{0.277\times10^3\times299.7}=2.64\times10^{-3}mol$$

Idial gas equation

$Q=nC_v∆T$

$C_v=\frac{Q}{n∆T}$

$C_v=\frac{31.65}{2.64\times10^{-3}\times299.7}=40.002$

Gas relationship

$C_p-C_v=R$

$C_p=C_v+R$

$$C_p=40.002+0.277=40.279KJ/kg-K$$

(B)

Mass

$$m=\frac{PV}{RT}=\frac{517.11\times10^{3}\times0.425}{0.277\times10^3\times200.7}=3.95kg$$

(C)

$$V=\frac{nRT}{P}=\frac{2.64\times10^{-3}\times0.277\times10^{3}\times299.7}{517.11\times10^{3}}=4.23\times10^{-4}m^3$$