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  • An ideal gas undergoes a reversible adiabatic expansion in a piston-cylinder system. The initial pressure is <img alt="\mathrm{3 \mathrm{~atm}}" src="https://entrancecorner.oncodecogs.com/gif.latex

An ideal gas undergoes a reversible adiabatic expansion in a piston-cylinder system. The initial pressure is \mathrm{3 \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 1.4 .

Option: 1

1.15 atm


Option: 2

1.13 atm


Option: 3

2.5 atm


Option: 4

1.2 atm


Answers (1)

best_answer

Given data: Initial pressure \mathrm{\left(P_i\right)=3} 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)=1.4}

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 \mathrm{~atm}) \cdot(30 \text { liters })^{1.4}}{(60 \text { liters })^{1.4}} \approx 1.13 \mathrm{~atm} }

Therefore, the final pressure of the gas is approximately \mathrm{ 1.13 \mathrm{~atm}.}

so, the correct option is 2

Posted by

Shailly goel

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