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for question 8.31, the solutions manual multiplies 5/2 R and gets 20.8J*mol^-1*C^-1 and then proceeds to cancel the unit C^-1 with the C of the delta T, but isn't the gas constant in units of J*mol^-1*K^-1*? so shouldn't there be a conversion to K of delta t somewhere in the solution?
The constant R is the same, whether you look at temperature in oCelsius or Kelvin. We are looking at a "change in temperature," and since the relationship is K = oC + 273.15, that change in temperature would be still be the same whether in Celsius or Kelvin.
This is a little bit tricky. So as you know, 5/2R in this case results in heat capacity. You are right that for R=8.314 K/molK which is not the same as 8.314J/molC because it depends on temperature (not change in temperature). However, after multiplying R with 5/2, you get heat capacity which depends on the change in temperature, then oC or K will not make any difference.
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