To find the change in enthalpy, ΔH, you need to use the equation:
ΔH = q + W
where q is the heat transferred and W is the work done.
Given that the work done is 2.3 kJ, you already have the value for W.
To find q, you can use the equation:
q = nCvΔT
where n is the number of moles, Cv is the molar heat capacity at constant volume, and ΔT is the change in temperature.
You've already calculated n to be 0.50075 moles.
The change in temperature, ΔT, can be found by converting the initial and final temperatures from Celsius to Kelvin:
ΔT = Tf - Ti
Initial temperature, Ti = 51 °C = 51 + 273.15 = 324.15 K
Final temperature, Tf = 55981.3 K (as you have calculated correctly)
Now, let's calculate q:
q = (0.50075 mol) * (3R/2) * (55981.3 K - 324.15 K)
Using R = 8.314 J/(mol·K), plug in the values and calculate q.
Once you have q, you can find ΔH using the equation:
ΔH = q + W
Substitute the values of q and W that you have calculated to find the correct value of ΔH.