A monoatomic ideal gas, initially at temperature T1, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If L1 and L2 are the lengths of the gas column before and after expansion respectively, then T1/T2 is given by

  • Option 1)

    (L1/L2) ^(2/3)

  • Option 2)

    L1/L2

  • Option 3)

    L2/L1

  • Option 4)

    (L2/L1) ^(2/3)

 

Answers (1)

As we discussed in concept

Equation of state -

dQ= 0

n\, C_{V}\, dT+PdV= 0
 

- wherein

On solving

\gamma \frac{dV}{V}+\frac{dP}{P}= 0

\Rightarrow PV^{\gamma }= constant

 

 For adiabatic process:

TV^{r-1}\:=\:constant.

T_{1}.L_{1}^{r-1}\:=\:T_{2}L_{2}^{r-1}

\frac{T_{1}}{T_{2}}\:=\:(\frac{L_{2}}{L_{1}})^{r-1}\:=\:(\frac{L_{2}}{L_{1}})^{\frac{2}{3}}

\therefore\:r_{monoatomic}\:=\:\frac{2}{3}


Option 1)

(L1/L2) ^(2/3)

This option is incorrect.

Option 2)

L1/L2

This option is incorrect.

Option 3)

L2/L1

This option is incorrect.

Option 4)

(L2/L1) ^(2/3)

This option is correct.

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