a litre of air initially at 327 degree centigrade is first cooled at a temperature at 27 degree centigrade , the volume remaining constant and compressed to its original pressure . Find the final volume of air .

Open in App

Solution

$S i n c e t h e v o l u m e r e m a i n s c o n s \tan t w h e n 1 l i t r e o f a i r i s c o o l e d f r o m T_{0} = (273 + 327) = 600 K t o T_{1} = (273 + 27) = 300 K, s o P α T . T h e r e f o r e \frac{P_{0}}{T_{0}} = \frac{P_{1}}{T_{1}} i . e . \frac{P_{0}}{600} = \frac{P_{1}}{300} o r P_{1} = \frac{P_{0}}{2} N o w w h e n P_{2} = P_{0} t h e n b y B o y l e' s l a w w e g e t; P_{0} V_{2} = \frac{P_{0}}{2} V_{0} o r V_{2} = \frac{V_{0}}{2} T h u s t h e f i n a l v o l u m e o f a i r i s \frac{V_{0}}{2} = \frac{1}{2} l i t r e . o r$

Suggest Corrections

Similar questions

Q. Pressure remaining the constant, the volume of a given mass of ideal gas increases for every degree centigrade rise in temperature by a definite fraction of its volume at:

Pressure remaining the same, the volume of a given mass of an ideal gas increases for every degree centigrade rise in temperature by definite fraction of its volume at

Q. At what temperature in degree centigrade will the volume of the gas be doubled at

0^{\circ} C

and constant pressure?

Q. What is the volume of 2g

O_{2}

at 0 degree centigrade and 760 mm pressure of Hg?

Q. At what centigrade temperature will a given volume of a gas at

0^{\circ}

C becomes double if pressure remains constant?

Join BYJU'S Learning Program

a litre of air initially at 327 degree centigrade is first cooled at a temperature at 27 degree centigrade , the volume remaining constant and compressed to its original pressure . Find the final volume of air .

Since the volume remains constant when 1litre of air is cooled from T0=273+327=600K to T1=273+27=300K, so P α T.Therefore P0T0=P1T1i. e. P0600=P1300or P1=P02Now when P2=P0 then by Boyle's law we get; P0V2= P02V0or V2=V02Thus the final volume of air is V02=12litre.or