According to Mayer\'s relationship, the molar specific heat for an ideal gas It
ID: 717912 • Letter: A
Question
According to Mayer's relationship, the molar specific heat for an ideal gas It can be expressed as: Cp, m = Cv, m + R For ethanol (CH3CH2OH) in gaseous form, the specific heat in J / mol K is approximately 7.7R for temperatures between 0 and 100 ° C and low pressures. Calculate q, w, U and H, for the reversible adiabatic expansion of 10 mg of ethanol at 20 torr from a volume of 220 to 500 cm3. It assumes an ideal behavior. Consider Cp, m and a Cv, m constants and lean on the following expression of the first law to solve the problem
-R T1 V1Explanation / Answer
Specific heat capacity at constant pressure of gaseous ethanol
Cp = 7.7 x 8.314 J/mol·K = 64.0178 J/mol·K
From Mayor's formula
Cv = Cp - R = 7.7 R - R = 6.7 R
Specific heat capacity ratio n = Cp/Cv = 7.7/6.7 = 1.15
Moles of ethanol = mass/molecular weight
= 10 mg / (46.07 mg/mmol) = 0.2171 mmol x 1mol/1000mmol
m = 2.17 x 10^-4 mol
Pressure P1 = 20 torr
Volume V1 = 220 cm3
Volume V2 = 500 cm3
Pressure P2 =?
For adiabatic and reversible expansion process
P1V1n = P2V2n
20 x 2201.15 = P2 x 5001.15
P2 = 7.78 torr
Initial temperature for ideal gas equation
T1 = P1V1/mR
= (20 torr x 1atm/760torr x 220 cm3 x 1L/1000cm3) / (2.17 x 10^-4 mol x 0.0821 L-atm/mol-K)
= 324.96 K
T2 = P2V2/mR
= (7.78 torr x 1atm/760torr x 500 cm3 x 1L/1000cm3) / (2.17 x 10^-4 mol x 0.0821 L-atm/mol-K)
= 287.30 K
For adiabatic process
q = 0
Work done
W = mR(T2 - T1) / (n - 1)
= 2.17 x 10^-4 mol x 8.314 J/mol·K x (287.30 - 324.96)K / (1.15 - 1)
= - 0.453 J
Change in internal energy U = q + W = 0 - 0.453
U = - 0.453 J
Change in enthalpy H = m x Cp x (T2-T1)
= 2.17 x 10^-4 mol x 64.0178 J/mol·K x (287.30 - 324.96)K
= - 0.523 J