Question

A quantity of dry air (y = 1.4) at 15°C is

adiabatically compressed to half its volume.

Calculate the final temperature.​

Answer 1

Answer:

T₂ = 19.79 ⁰C

Explanation:

Before adiabatic compression,

T₁ = 15⁰ C

V₁ = v

After the adiabatic compression,

T₂ = ?

V₂ =  0.5 v

The ideal gas equation for adiabatic compression( y = 1.4 )

$PV^{1.4} = constant$

So we can derive the formula ,

$\frac{T_{2} }{T_{1} } = ( \frac{V_{1} }{V_{2} } )^{y - 1}$

$T_{2} = 15 * ( \frac{v}{0.5 v} )^{1.4 - 1}$

T₂ = 19.79 ⁰C