The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol.K). When the temperature increases by 100k, the change in molar specific enthalpy is ___ J/mol.:
Question
The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol.K). When the temperature increases by 100k, the change in molar specific enthalpy is ___ J/mol.:
Solution
To solve this problem, we need to use the formula for the change in molar specific enthalpy (∆H) at constant pressure, which is given by:
∆H = Cp * ∆T
Where: Cp is the molar specific heat at constant pressure, ∆T is the change in temperature.
For an ideal gas, the relationship between Cp and Cv (molar specific heat at constant volume) is given by:
Cp = Cv + R
Where: R is the universal gas constant.
Given that Cv = 2.5R, we can substitute this into the equation to find Cp:
Cp = 2.5R + R = 3.5R
Now we can substitute Cp = 3.5R and ∆T = 100K into the equation for ∆H:
∆H = Cp * ∆T = 3.5R * 100K
Substituting R = 8.314 J/mol.K, we get:
∆H = 3.5 * 8.314 J/mol.K * 100K = 2910.9 J/mol
So, the change in molar specific enthalpy when the temperature increases by 100K is 2910.9 J/mol.
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