Calculate the difference between (C_{P}) and (C_{V}) for a copper block having isothermal compressibility (alpha=0.837 times 10^{-11}

Question:

Calculate the difference between \(C_{P}\) and \(C_{V}\) for a copper block having isothermal compressibility \(\alpha=0.837 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{N}\) and volume expansivity \(\beta=54.2 \times 10^{-6} \mathrm{~K}^{-1}\) at \(227^{\circ} \mathrm{C}\), given that the specific volume of copper is \(7.115 \times 10^{-3} \mathrm{~m}^{3} / \mathrm{kmol}\). If \(C_{P}\) for copper is \(26.15 \mathrm{~J} / \mathrm{mol}-\mathrm{K}\) at this temperature, then what percentage of error would be made in \(C_{V}\) if \(C_{P}\) is assumed to be equal to \(C_{V}\) ?

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