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Question
The difference between Cp and Cv can be derived using H=U+PV. Calculate the difference between Cp and Cv for 10 moles of an ideal gas.
The difference between Cp and Cv can be derived using H=U+PV. Calculate the difference between Cp and Cv for 10 moles of an ideal gas.
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Solution
The correct option is D 83.14 J/K
From first law, ΔU=q+w
For a constant volume system, w = 0 and ΔU=nCvdT = heat at constant volume
where n is the number of moles of the gas
Similarly, ΔH=nCpdT = Heat at constant pressure
We know, Cp− Cv = R for 1 mole of a gas
Similarly, Cp− Cv = nR for n mole of a gas
Cp− Cv =10×8.314 J mol−1 K−1
= 83.14 J/K
From first law, ΔU=q+w
For a constant volume system, w = 0 and ΔU=nCvdT = heat at constant volume
where n is the number of moles of the gas
Similarly, ΔH=nCpdT = Heat at constant pressure
We know, Cp− Cv = R for 1 mole of a gas
Similarly, Cp− Cv = nR for n mole of a gas
Cp− Cv =10×8.314 J mol−1 K−1
= 83.14 J/K
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