Respuesta :
Explanation:
The given data is as follows.
P = 1 bar, T = 298 K
For [tex]CO_{2}[/tex]; [tex]V_{1C} = 0.7 m^{3}[/tex]
For [tex]N_{2}[/tex]; [tex]V_{1N} = 0.3 m^{3}[/tex]
Therefore, final volume will be as follows.
[tex]V_{1C} + V_{1N} = 1 m^{3} = V_{2}[/tex]
Hence, [tex]V_{2} = 1 m^{3}[/tex]
Formula for change in entropy is as follows.
dS = [tex]nR ln (\frac{V_{2}}{V_{1}})[/tex]
For [tex]CO_{2}[/tex], [tex]PV_{1C} = nRT[/tex]
or, [tex]nR = \frac{PV_{1C}}{T}[/tex]
= [tex]\frac{10^{5} \times 0.7}{298}[/tex]
= 234.89
[tex]dS_{CO_{2}} = 234.89 \times \frac{1}{0.7}[/tex]
= 83.77 J/K
For [tex]N_{2}[/tex], nR = [tex]\frac{P_{1}V_{1}N}{T}[/tex]
= [tex]\frac{10^{5} \times 0.3}{298}[/tex]
= 100.67
[tex]dS_{N_{2}} = 100.67 ln (\frac{1}{0.3})[/tex]
= 121.20 J/K
Now, total change in the entropy is calculated as follows.
dS = [tex]dS_{CO_{2}} + dS_{N_{2}}[/tex]
= (83.77 + 121.20) J/K
= 204.97 J/K
Thus, we can conclude that the change in entropy is 204.97 J/K.
Entropy change will be 204.97 J/K.
Firstly, let's write the given values:
Since, it's an ideal gas therefore;
- P=1 bar
- T=298 K
- For CO₂= [tex]V_{CO_2} = 0.7m^3[/tex]
- For N₂= [tex]V_{N_2}=0.3 m^3[/tex]
Thus, the final volume will be V₂= [tex]0.7+0.3=1m^3[/tex]
What does change in entropy mean?
Entropy change can be defined as the change in the state of disorder of a thermodynamic system that is associated with the conversion of heat or enthalpy into work.
Entropy change can be calculated by using the given formula:
[tex]\text{dS}=n R ln \frac{V_2}{V_1}[/tex]
⇒For CO₂,
From ideal gas equation it is known that: pV=nRT
∴ nR=pV/T
[tex]nR=\frac{10^5 *0.7}{298} =234.89[/tex]
So, entropy change for CO₂ will be:
[tex]dS_{CO_2}=234.89ln (\frac{1}{0.7} )=83.77J/K[/tex]
⇒For N₂,
[tex]nR=\frac{10^5*0.3}{298} =100.67[/tex]
So, entropy change for N₂ will be:
[tex]dS_{N_2}=100.67 ln(\frac{1}{0.3}) =121.20 J/K[/tex]
Now, total entropy change can be calculated as:
[tex]dS_{Total}=dS_{CO_2}+dS_{N_2}\\\\=83.77+121.20\\\\=204.97 J/K[/tex]
Thus, entropy change will be 204.97 J/K.
Learn more:
brainly.com/question/23084720
