The correct answer to this question is C. 5/4 R.
What is the Molar heat capacity (Cm) of gas for the process?
First, convert the heat absorbed from calories to Joules:
100 cal * 4.184 J/cal = 418.4 J
2. Apply the first law of thermodynamics:
For a closed system undergoing a change in temperature, the first law of thermodynamics states:
ΔU = Q + W
Where:
ΔU is the change in internal energy
Q is the heat absorbed
W is the work done by the system
For an ideal gas at constant pressure, the change in internal energy is related to the change in temperature by:
ΔU = nCvΔT
Where:
n is the number of moles of gas
Cv is the molar heat capacity at constant volume
ΔT is the change in temperature
Substitute the expressions for ΔU and Q in the first law equation:
nCvΔT = 418.4 J + 209 J
Rearrange for Cv:
Cv = (418.4 J + 209 J) / (nΔT)
5. Molar heat capacity at constant pressure (Cp):
For a diatomic ideal gas, the relationship between Cp and Cv is:
Cp = Cv + R
Where:
R is the gas constant
Substitute the expression for Cv from step 4:
Cp = [(418.4 J + 209 J) / (nΔT)] + R
Therefore, the molar heat capacity (Cp) of the gas for this process is a constant multiple of R. Since the work done (W) is positive, Cp will be greater than Cv. The only option that fits this observation is 5/4 R.