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Calculate the average energy and specific heat capacity of a system containing 1000 molecules of an ideal gas at a temperature of 300 K, when the gas is subjected to an isochoric process and its volume remains constant at 2.5 L.

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To calculate the average energy and specific heat capacity of the system, we first need to determine the degrees of freedom for the gas molecules. Since it is an ideal gas, we can assume that the gas molecules are non-linear and have 3 translational degrees of freedom.For an isochoric process, the volume remains constant, and only the translational degrees of freedom contribute to the internal energy and specific heat capacity.1. Average energy:The average energy  E  of an ideal gas can be calculated using the equipartition theorem, which states that the average energy per molecule is given by:E =  f/2  * k * Twhere f is the degrees of freedom  f = 3 for translational degrees of freedom , k is the Boltzmann constant  1.38  10^-23  J/K , and T is the temperature in Kelvin.E =  3/2  *  1.38  10^-23  J/K  * 300 KE  6.21  10^-21  JThe average energy per molecule is approximately 6.21  10^-21  J.2. Specific heat capacity:The specific heat capacity at constant volume  Cv  for an ideal gas can be calculated using the following formula:Cv =  f/2  * Rwhere f is the degrees of freedom  f = 3 for translational degrees of freedom  and R is the universal gas constant  8.314 J/mol K .Cv =  3/2  * 8.314 J/mol KCv  12.471 J/mol KThe specific heat capacity at constant volume for the gas is approximately 12.471 J/mol K.Now, we have the average energy per molecule and the specific heat capacity at constant volume for the system.

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