Question

Temperature and pressure of a region upstream of a shockwave are 295 K and 1.01* 109 N/m². Just downstream the shockwave, the temperature and pressure changes to 800 K and 8.74 * 10 N/m². Determine the change in following across the shockwave: a. Internal energy b. Enthalpy c. Entropy

Answer 1

change in internal energy 3.62*10^5 J kg^{-1}

change in enthalapy 5.07*10^5 J kg^{-1}

change in entropy 382.79 J kg^{-1} K^{-1}

Step-by-step explanation:

adiabatic constant
`\gamma =1.4`

specific heat is given as
`=(\gamma R)/(\gamma -1)`

gas constant =287 J⋅kg−1⋅K−1

`Cp = (1.4*287)/(1.4-1) = 1004.5 Jkg^(-1) k^(-1)`

specific heat at constant volume

`Cv = (R)/(\gamma -1) = (287)/(1.4-1) = 717.5 Jkg^(-1) k^(-1)`

change in internal energy
`= Cv(T_2 -T_1)`

`\Delta U = 717.5 (800-295)  = 3.62*10^5 J kg^(-1)`

change in enthalapy
`\Delta H = Cp(T_2 -T_1)`

`\Delta H = 1004.5*(800-295) = 5.07*10^5 J kg^(-1)`

change in entropy

`\Delta S =Cp ln((T_2)/(T_1)) -R*ln((P_2)/(P_1))`

`\Delta S =1004.5 ln((800)/(295)) -287*ln((8.74*10^5)/(1.01*10^5))`

`\Delta S = 382.79 J kg^(-1) K^(-1)`