A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $1.4$ . Vessel is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by :
( $R =$ universal gas constant)

Question

A thermally insulated vessel contains an ideal gas of molecular mass

M

and ratio of specific heats

1.4

. Vessel is moving with speed

v

and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by :
(

R =

universal gas constant)

Aicharya · Accepted Answer

KE of the vessel = 1 2 m v 2 When the vessel is suddenly stopped, the ordered motion of the gas molecules is converted into disordered motion of the molecules increasing thereby the internal energy of the gas. Thus, &#8710; U = n C v &#8710; T = 1 2 m v 2 = 1 2 n M v 2 Where n is number of moles of the gas in the vessel and M is molecular weight of the gas. &#8756; &#160; &#160; &#8710; T = M v 2 2 C v As C v = R &#947; - 1 &#8756; &#160; &#160; &#8710; T = M v 2 ( &#947; - 1 ) 2 R = M v 2 ( 1 . 4 - 1 ) 2 R = M v 2 5 R

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1 . 4 .…

Solution