Answer to Question #89712 in Molecular Physics | Thermodynamics for Shivam Nishad

Question

One mole of oxygen at STP is adiabatically compressed to 5 atm. Calculate the final temperature. Take y = 1.4 and R= 8.31 J mol^-1 K^-1

Answer 1

The relation between pressure and volume in an adiabatical process is

$$P V^{\gamma} = \mathrm{const}$$

Using

$$PV = \nu RT$$

we obtain

$$P \bigg(\frac{T}{P}\bigg)^\gamma = \frac{T^{\gamma}}{P^{\gamma-1}}= \mathrm{const}$$

or

$$\frac{T_{\mathrm{final}}} {T_{\mathrm{initial}}}=\bigg(\frac{P_{\mathrm{final}}}{P_{\mathrm{initial}}}\bigg)^{\frac{\gamma-1}{\gamma}}$$

so

$$T_{\mathrm{final}} = T_{\mathrm{initial}} 5^{0.4/1.4} = 1.58 T_{\mathrm{initial}} = 432\, \mathrm{K}$$