Thermodynamics of a adiabatic system with degrees of freedom

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In an adiabatic process where 16 J of work is done on each mole of a gas with 5 degrees of freedom, the temperature change can be calculated using the first law of thermodynamics and the formula for the variation of internal energy of an ideal gas. The relationship between work done and temperature change is expressed as ΔU = Q - W, where Q is zero in an adiabatic process. For a gas with 5 degrees of freedom, the change in internal energy is directly related to the temperature change by the equation ΔU = (f/2) * n * R * ΔT. This leads to the conclusion that the temperature change is 6.4/R (K). Understanding these principles is essential for solving problems related to adiabatic processes in thermodynamics.
heyhey1233
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In an adiabatic process 16 J of work are done on each mole
of a gas. If the gas has 5 degrees of freedom, how much
does its temperature change? Answer in terms of R


I know the answer is 6.4/R (K), but don't quite sure understand the the theory or math behind it.
 
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You can use the first law (principle) and formula for the variation of internal energy of an ideal gas.
 

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