First slide

Thermodynamic processes

Question

An ideal gas at $27^{o} C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. If $γ = \frac{5}{3}$ , then the rise in temperature is

Moderate

A

450 K
B

375 K
C

225 K
D

405 K

Solution

$\begin{array}{l} \frac{T_{2}}{T_{1}} = {(\frac{V_{1}}{V_{2}})}^{γ - 1} \Rightarrow T_{2} = 300 {(\frac{27}{8})}^{\frac{5}{3} - 1} = 300 {(\frac{27}{8})}^{\frac{2}{3}} \\ = 300 {\{{(\frac{27}{8})}^{1 / 3}\}}^{2} = 800 {(\frac{3}{2})}^{2} = 675 K \\ \Rightarrow ΔT = 675 - 300 = 375 K \end{array}$

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