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The volume of an ideal gas (γ = 1.5) is changed adiabatically from 4.00 litres to 3.00 litres. Find the ratio of (a) the final pressure to the initial pressure and (b) the final temperature to the initial temperature.

The volume of an ideal gas (γ = 1.5) is changed adiabatically from 4.00 litres to 3.00 litres. Find the ratio of (a) the final pressure to the initial pressure and (b) the final temperature to the initial temperature.

Grade:upto college level

1 Answers

Kevin Nash
askIITians Faculty 332 Points
6 years ago
Sol. γ = 1.5 Since it is an adiabatic process, So PV^γ = const. (a) P base 1V base 1^γ = P base 2V base 2^γ Given V base 1 = 4 L, V base 2 = 3 L, P base 2/P base 1 = ? ⇒ P base 2/P base 1 = (V base 1/V base 2)^γ = (4/3)^1/5 = 1.5396 = 1.54 (b) TV^γ-1 = Const. T base 1/V base 1)^γ-1 = T base 2/V base 2)^γ-1 ⇒ T base 1/T base 2 = (V base 1/V base 2)^γ-1 = (4/3)^0.5 = 1.154

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