cp=cv+R is only valid for ideal gases. The assumption that solid steel is an ideal gas is dangerous. For solid(and liquid) stuff you have only one kind of heat capacity, since pressure has no effect on volume.
If lans would read my post above he would find 99% of what's missing. (I calculated +1.2kj/K entropy, using his numbers). The remaining stuff will depend on the parameters / table values. (afaik steel =0.5kj/kg)
