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

1. ((γ−1)/(2γR)) Mv² K
2. (γM²v/(2R)) K
3. ((γ−1)/2R) Mv² K
4. ((γ−1)/(2(γ+1)R)) Mv² K

Correct answer: ((γ−1)/2R) Mv² K

Solution

The correct option is derived from the principle of conservation of energy, where the kinetic energy of the gas is converted into internal energy, leading to an increase in temperature. The relationship incorporates the specific heat ratio γ and the ideal gas law, resulting in the expression for temperature change being proportional to the kinetic energy per unit mass.

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