The average degree of freedom per molecule for a gas is 6. The gas performs 25 J of work when it expands at constant pressure. The heat absorbed by the gas is:
Correct answer: B. 100 J
- A. 75 J
- B. 100 J
- C. 150 J
- D. 125 J
Explanation
According to the first law of thermodynamics, the change in internal energy (ΔU) is equal to the heat absorbed (Q) minus the work done (W), i.e., ΔU = Q - W. For a gas with an average degree of freedom per molecule, the relation for the specific heat capacity at constant pressure (Cp) can be derived considering the degrees of freedom. With 6 degrees of freedom, Cp = (7/2)R per mole. The work done by the gas at constant pressure is given as 25 J. By applying the first law and considering the relationship between Cp, Q, and W, the heat absorbed by the gas is calculated to be 100 J. Options A, C, and D do not align with this derivation, leading to incorrect conclusions about the heat absorbed.
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About Molar Specific Heat of a Gas
Molar specific heat is the heat required to raise the temperature of one mole of a gas by one kelvin, expressed through Q = nCΔT. Questions compare the constant volume value Cv with the constant pressure value Cp, apply the ideal gas relation Cp − Cv = R, and identify how the thermodynamic process affects heat capacity.
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