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Question
An ideal gas of volume 2 L is adiabatically compressed to (1/10)th of its initial volume. Its initial pressure is 1.01 x 105 Pa, calculate the final pressure. (Given 𝛾 = 1.4)
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Solution
Given:
Vi = 2 L, Vf = `("V"_"i")/10 ⇒ ("V"_"i")/("V"_"f") = 10, "P"_"i" = 1.01 xx 10^5` Pa, γ = 1.4
To find: Final pressure (pf)
Formula: For adiabatic process: `"p"_"f" "V"_"f"^γ = "p"_"i""V"_"i"^γ`
Calculation:
From formula,
pf = pi × `("V"_"i"/"V"_"f")^γ`
= 1.01 × 105 × (10)1.4
= antilog {log (1.01) + 1.4 × log (10)} × 105
= antilog {0.0043 + (1.4 × 1)} × 105
= antilog {1.4043} × 105
= 2.537 × 106 = 25.37 × 105 Pa
The final pressure (pf) is 25.37 × 105 Pa
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