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

Engineering

Physics

Thermodynamics

Degree of Freedom Internal Energy of Gas and Specific Heat Capacity of Gases

Question

The thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heat $γ$ . It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by :

$\frac{(γ - 1)}{2 γ R} M v^{2} K$

$\frac{(γ - 1)}{2 (γ + 1) R} M v^{2} K$

$\frac{(γ - 1)}{2 R} M v^{2} K$

$\frac{γ M v^{2}}{2 R} K$

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$\frac{1}{2}M{\nu ^2} = {C_v}.\Delta T$

$\frac{1}{2}M{\nu ^2} = \frac{R}{{\gamma - 1}}.\Delta T$

$\Delta T = \frac{{M{\nu ^2}(\gamma - 1)}}{{2R}} = \frac{{(\gamma - 1)M{\nu ^2}}}{{2R}}$