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The gas constant for one kg of oxygen is...

The gas constant for one kg of oxygen is 259.3 `J kg ^(-1) K ^(-1).` Find the value of `C_(p) and C_(v) ` in `J mol ^(-1) K ^(-1) gamma = 1.4`

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To find the values of \( C_p \) and \( C_v \) for one kg of oxygen in \( J \, mol^{-1} \, K^{-1} \) given that the gas constant \( R = 259.3 \, J \, kg^{-1} \, K^{-1} \) and \( \gamma = 1.4 \), we can follow these steps: ### Step 1: Calculate the number of moles of oxygen in 1 kg The molecular mass of oxygen (O₂) is approximately 32 g/mol (16 g/mol for each oxygen atom). To find the number of moles in 1 kg (1000 g) of oxygen: \[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{1000 \, g}{32 \, g/mol} = 31.25 \, mol ...
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