Thermodynamics change in internal energy

[tom2tom]

1. A gas bottle with a volume of 0.1 m3 contains 0.4 kg of a gas at a pressure of 7
MN/m2 and a temperature of 150 ºC. For this gas Cp = 10.54 kJ/kg K. Calculate
the changes in internal energy when temperature is raised to 500K
Given answer: 362 kJ



2. pV=mRT pv=RT
mCpdT=dH
mCvdT=dU
dq-dw=du



3. so I've been struggling with this for a while. i know that du=dq as there is no net work when volume is constant.
initially i used p1V1/mT1=R and then i used Cp=R+Cv to find Cv. From there i used the equation mCvdT=dU. however this doesn't give the correct answer.

ive been trying a few other ways as well but they haven't worked. is there some assumption i can make etc...?

 

[Andrew Mason]

Try calculating the number of moles using n = PV/RT with units in MKS and a gas constant of R = 8.314 J/K mol. I assume 7 MN/m^2 means 7x10^6 Pa.

Then work out the ratio of moles to kg. to determine what the Cp is in terms of J/mole K. Subtract R from that to get Cv.

I get n = 199 moles and Cv = 12.87 J/mol K, which gives an answer:

$$\Delta U = nC_v\Delta T = 199 \times 12.87 \times 77 = 197.2 KJ$$

So I think the answer given is wrong.

AM