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  • An ideal gas undergoes a reversible adiabatic expansion in a piston-cylinder system. The initial pressure is <img alt="3.0 \mathrm{~atm}" src="https://entrancecorner.oncodecogs.com/gif.latex?3.0%20

An ideal gas undergoes a reversible adiabatic expansion in a piston-cylinder system. The initial pressure is 3.0 \mathrm{~atm}, and the initial volume is 30 liters. During the expansion, the volume increases to 60 liters. Calculate the final pressure of the gas. Given the heat capacity ratio \mathrm{\left(C_p / C_v\right)} for the gas is 1.25 .
 

Option: 1

3 \mathrm{~atm}


 


Option: 2

4 \mathrm{~atm}
 


Option: 3

1.75 \mathrm{~atm}
 


Option: 4

1.5 \mathrm{~atm}


Answers (1)

best_answer

Given data:

Initial pressure \mathrm{\left(P_i\right)=3.0\: atm}

Initial volume \mathrm{\left(V_i\right)=30} liters

Final volume \mathrm{\left(V_f\right)=60} liters

Heat capacity ratio \mathrm{\left(C_p / C_v\right)=1.25}

For a reversible adiabatic process, the relationship between initial and final conditions is given by:

\mathrm{ P_i \cdot V_i^\gamma=P_f \cdot V_f^\gamma }
Solving for the final pressure \mathrm{ \left(P_f\right) : }
\mathrm{ P_f=\frac{P_i \cdot V_i^\gamma}{V_f^\gamma} }
Substituting the values and solving:

\mathrm{ P_f=\frac{(3.0 \mathrm{~atm}) \cdot(30 \text { liters })^{1.25}}{(60 \text { liters })^{1.25}} \approx 1.50 \mathrm{~atm} }
Therefore, the final pressure of the gas is approximately \mathrm{ 1.50 \mathrm{~atm} }.

So, correct option is 4

Posted by

Shailly goel

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