Question

Carbon dioxide initially at 50 kPa, 400 K, undergoes a process in a closed system until its pressure and temperature are 2 MPa and 800 K, respectively. Assuming an ideal gas behaviour, find the entropy change of the carbon dioxide by assuming that the specific heats are constant. For the gas, take Cp = 0.846 kJ/kg.K and R = 0.1889 kJ/kg.K

Answer 1

`$ S_2 - S_1 = -0.1104 \: \: kJ/kg.K$`

The entropy change of the carbon dioxide is -0.1104 kJ/kg.K

Step-by-step explanation:

We are given that carbon dioxide undergoes a process in a closed system.

We are asked to find the entropy change of the carbon dioxide with the assumption that the specific heats are constant.

The entropy change of the carbon dioxide is given by

`$ S_2 - S_1 = C_p \ln ((T_2)/(T_1)) - R\ln ((P_2)/(P_1)) $`

Where Cp is the specific heat constant

Cp = 0.846 kJ/kg.K

R is the universal gas constant

R = 0.1889 kJ/kg.K

T₁ and T₂ is the initial and final temperature of carbon dioxide.

P₁ and P₂ is the initial and final pressure of carbon dioxide.

`$ S_2 - S_1 = 0.846 \ln ((800)/(400)) - 0.1889\ln ((2000)/(50)) $`

`$ S_2 - S_1 = 0.846(0.69315) - 0.1889(3.6888) $`

`$ S_2 - S_1 = 0.5864 - 0.6968 $`

`$ S_2 - S_1 = -0.1104 \: \: kJ/kg.K$`

Therefore, the entropy change of the carbon dioxide is -0.1104 kJ/kg.K