If 1 mole of an ideal gas is heated at constant volume so that its temperature rises by delta T, then first law of thermodynamics can be written as:
Correct answer: C. ΔU = CvΔT
- A. ΔU + Cv = ΔT
- B. ΔU = Cv-ΔT
- C. ΔU = CvΔT
- D. ΔU=Cv+ΔT
Explanation
Isochoric Process:The thermodynamics process during which the volume of the system remains constant is called isochoric process.As the volume is constant then work done will be zero. ΔW=0Using the first law of thermodynamics equation:ΔQ=ΔU+ΔWΔQ=ΔU eq (1)The heat given is Q,which is used to provide the Molar specific heat at constant volume which is given as CvΔT.Eq (1) becomes ΔU=CvΔTHence, C is the correct option.
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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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