Monoatomic, diatomic and triatomic gases whos | vedclass

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(A) For an adiabatic process, the relation between pressure and volume is given by $P V^{\gamma} = 	ext{constant}$.Since the initial pressure $P_1$ a

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If the compression is adiabatic then monoatomic gas will have maximum final pressure.

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(A) For an adiabatic process, the relation between pressure and volume is given by $P V^{\gamma} = 	ext{constant}$.Since the initial pressure $P_1$ and initial volume $V_1$ are the same for all gases, the final pressure $P_2$ after the volume is compressed to $V_2 = V_1/2$ is given by $P_2 = P_1 (V_1/V_2)^{\gamma} = P_1 (2)^{\gamma}$.The adiabatic index $\gamma$ is defined as $C_p/C_v$. For a monoatomic gas, $\gamma = 5/3 \approx 1.67$. For a diatomic gas, $\gamma = 7/5 = 1.4$. For a triatomic gas, $\gamma$ is even lower (e.g., $4/3 \approx 1.33$ for non-linear).Since $P_2 = P_1 \cdot 2^{\gamma}$, the gas with the highest value of $\gamma$ will result in the highest final pressure $P_2$.Therefore, the monoatomic gas will have the maximum final pressure.

Monoatomic, diatomic and triatomic gases whose initial volume and pressure are same, are compressed till their volume becomes half the initial volume.

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