Question
Given below are two statements:
Statement I: For an ideal gas, heat capacity at constant volume is always greater than the heat capacity at constant pressure.
Statement II : In a constant volume process, no work is produced and all the heat withdrawn goes into the chaotic motion and is reflected by a temperature increase of the ideal gas.
In the light of the above statements, choose the correct answer from the options given below
Options
Solution
Sol. [Key Concept: $C_{p} = C_{v} + R \Rightarrow \ C_{p} > C_{v}$, so Statement I is false; at constant $V$, $w = 0$ and all heat raises $T$ (II true).]
From first law of thermodynamics
$$\Delta U = q + w $$constant volume $w = 0$
$$\Delta U = q $$Also $C_{P} = C_{V} + R$
$C_{P} =$ heat capacity at constant pressure
$C_{v} =$ Heat capacity at constant volume.
$R =$ constant
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