Question 507: Thermodynamics & KTG

Question

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $$C$$ remains constant. If during this process the relation of pressure $$P$$ and volume $$V$$ is given by $$P{V^n} = $$ constant, then $$n$$ is given by (Here $${C_p}$$ and $${C_v}$$ are molar specific heat at constant pressure and constant volume, respectively:

Accepted Answer

For a  polytropic process
$$C = {C_v} + {R \over {1 - n}}$$
$$	herefore$$ $$C - {C_v} = {R \over {1 - n}}$$
$$	herefore$$ $$1 - n = {R \over {C - {C_v}}}$$
$$	herefore$$ $$1 - {R \over {C - {C_v}}} = n$$
$$	herefore$$ $$n = {{C - {C_v} - R} \over {C - {C_v}}}$$
$$ = {{C - {C_v} - {C_p} + {C_v}} \over {C - {C_v}}}$$
$$ = {{C - {C_p}} \over {C - {C_v}}}$$
( as $${C_p} - {C_{v = R}}$$ )

Answer

$$n = {{{C_p} - C} \over {C - {C_v}}}$$

Answer

$$n = {{C - {C_v}} \over {C - {C_p}}}$$

Answer

$$n = {{{C_p}} \over {{C_v}}}$$

Answer

$$n = {{C - {C_p}} \over {C - {C_v}}}$$

Thermodynamics & KTG

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