If 1 mole of an ideal gas is heated at constant volume, then:
Correct answer: B. ∆U=CV∆T
- A. ∆U=CV∆Q
- B. ∆U=CV∆T
- C. ∆T=CV∆U
- D. ∆U=Cp∆T
Explanation
In thermodynamics, when an ideal gas is heated at constant volume, the work done on the system is zero because the volume does not change. According to the first law of thermodynamics, the change in internal energy (∆U) is equal to the heat added to the system (∆Q) minus the work done (∆W), or ∆U = ∆Q - ∆W. At constant volume, ∆W = 0, so ∆U = ∆Q. Furthermore, ∆U is directly proportional to the change in temperature (∆T) through the heat capacity at constant volume (Cv), hence ∆U = Cv∆T. This is why option B is correct. Options A, C, and D incorrectly associate or apply the relationships between ∆U, ∆T, and Cv/Cp.
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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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