The pressure and density of a diatomic gas () change from () to () adiabatically. If , then what is — Thermodynamics and Thermochemistry Chemistry Question
Question
The pressure and density of a diatomic gas ($\gamma = 7/5$) change from ($P_1, d_1$) to ($P_2, d_2$) adiabatically. If $d_2/d_1 = 32$, then what is the value of $P_2/P_1$?
Answer: C
💡 Solution & Explanation
For an adiabatic process, $P V^\gamma = \text{constant}$. Since density $d \propto 1/V$, this translates to $P/d^\gamma = \text{constant}$. $P_2/P_1 = (d_2/d_1)^\gamma = (32)^{7/5} = (2^5)^{7/5} = 2^7 = 128$.
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