Question

What will be the volume of air at 327 °c if its volume at 27 °c is 1.5 m3 ?

Answer 1

Ideal gas equation is pv= mRT ,

In present case , pressure is constant. Thus ideal gas equation can be rewritten as

v/T = mR/p = constant ( since 'mass' and 'characteristic gas constant' are going to be remain same)

Thus,

T2/T1 = v2/v1 ( but in question it was given, v2 = 2×v1)

That is,

T2/(27+273) = 2× v1/v1 ( 273 is added with 27°C to convert in Kelvin)

T2=2×300

T2= 600 k i.e. 327°C( that is your final temperature)

Answer 2

Given,

$V_{1}$ = 1.5$m^{3}$

$T_{1}$ = $27^{0}C$ = 300K

$T_{2} = 327^{0}C$ = 600K

To Find,

Volume ($V_{2}$) of air at $327^{0}C$

Solution,

We know the ideal gas equation is given by,

     PV = mRT

From the ideal gas equation, we know that,

   $\frac{P_{1} V_{1} }{T_{1} } = \frac{P_{2} V_{2} }{T_{2} }$

And at constant pressure, it can be written as,

      $\frac{V_{1} }{T_{1} } = \frac{V_{2} }{T_{2} }$

Substituting the given values, we get,

      $\frac{1.5 }{300 } = \frac{V_{2} }{600} }$

Solving this we get,

      $V_{2}$ = 3$m^{3}$

The volume of air at 327 °c is 3 m3.