Question

At 27 degree celsius a gas was compressed to half of its volume to what temperature it must be heated so that it would occupy double its original volume

Answer 1

Given:

At 27 degree celsius a gas was compressed to half of its volume.

To find:

Temperature it must be heated so that it would occupy double its original volume

Calculation:

From ideal gas equation:

$\boxed{ \sf{PV = nRT}}$

Keeping P and n constant:

$\boxed{ \sf{ \therefore \: \dfrac{V}{T} = constant}}$

Let initial temperature be T;

In 1st case:

$\rm{ \therefore \: \dfrac{V}{T} = \dfrac{ (\frac{V}{2}) }{27 + 273} }$

$\rm{ = > \: \dfrac{V}{T} = \dfrac{ (\frac{V}{2}) }{300} }$

$\rm{ = > \: \dfrac{V}{T} = \dfrac{ V }{600} }$

$\rm{ = > \: T = 600 \: kelvin}$

In 2nd case:

$\rm{ \therefore \: \dfrac{V}{T} = \dfrac{ 2V }{T_{3}} }$

$\rm{ = > \: \dfrac{V}{600} = \dfrac{ 2V }{T_{3}} }$

$\rm{ = > \: T_{3} = 600 \times 2}$

$\rm{ = > \: T_{3} = 1200 \: kelvin}$

$\rm{ = > \: T_{3} = {927}^{ \circ}C }$

So, final answer is:

$\boxed{ \bf{\: T_{3} = {927}^{ \circ}C }}$