1.

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio o specific heats gamma. It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to surroundings, its temperature increases by

Answer»

`((gamma-1))/(2(gamma+1)R)Mv^(2)K`
`((gamma-1))/(2gammaR)Mv^(2)K`
`(gammaMv^(2))/(2R)K`
`((gamma-1))/(2R)Mv^(2)K`

SOLUTION :Kinetic energy of vessel = `(1)/(2)mv^(2)`
Increase in internal energy, `DeltaU=nC_(V)DeltaT`
where n is the number of moles of the GAS in vessel.
As the vessel is stopped suddenly, its kinetic energy is USED to increase the TEMPERATURE of the gas.
`therefore (1)/(2)mv^(2)=DeltaU=nC_(V)DeltaT=(m)/(M)C_(V)DeltaT(because n=(m)/(M))`
or `DeltaT=(Mv^(2))/(2C_(V))=(Mv^(2)(gamma-1))/(2R)K(because C_(V)=(R)/((gamma-1)))`


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