The specific heat of a gas in a polytropic process is given by:

\frac{R}{γ - 1} + \frac{R}{z - 1}

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\frac{R}{1 - γ} + \frac{R}{1 - z}

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\frac{R}{γ - 1} - \frac{R}{N - 1}

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\frac{R}{1 - γ} - \frac{R}{1 - N}

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Solution

The correct option is A $\frac{R}{γ - 1} + \frac{R}{z - 1}$
$d Q = n C d T$
$P V^{z} = c o n s t a n t$
$⟹ n C d T = d U + P d V$
$⟹ \int n C \cdot d T = \int n C_{V} \cdot d T + \int P \cdot d V$
$⟹ n C Δ T = n C_{V} Δ T + \int \frac{P V^{z}}{V^{z}} d V$
As, $P_{i} V_{i}^{z} = P_{f} V_{f}^{z}$
$i = i n i t i a l$
$f = f i n a l$
$⟹ \int \frac{P V^{z}}{V^{z}} \cdot d V = P V^{z} \int V^{- z} \cdot d V$
$⟹ \frac{- P_{i} V_{i}}{- z + 1} + \frac{P_{f} V_{f}}{- z + 1} = \frac{n R Δ T}{1 - z}$
As, $P V = n R T$
$Δ T = T_{f} - T_{i}$
$⟹ C = C_{v} + \frac{R}{1 - z}$ ;
As, $\frac{C_{p}}{C_{V}} = Y$
$C_{P} - C_{V} = R$
$⟹ C_{V} = \frac{R}{Y - 1}$ ,
So, $C = \frac{R}{Y - 1} + \frac{R}{1 - z}$

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Similar questions

For an ideal gas $(\frac{C_{P}}{C_{v}} = γ)$ ; of molar mass M, its specific heat capacity at constant volume is:

1 + r + r^{2} + r^{3} + . . . . . . . + r^{n} = (1 + r) (1 + r^{2}) (1 + r^{4}) (1 + r^{8})

1 + r + r^{2} + \dots . . . + r^{n} =

(1 + r) (1 + r^{2}) (1 + r^{4}) (1 + r^{8}),

n

R_{1} - C \equiv N + R_{2} M g B r (i) D r y e t h e r - ------ \to (i i) H_{3} O^{+} 1 - p h e n y l - 1 - p r o p a n o n e

R_{1}

R_{2}

For the relation $R_{1}$ defined on R by the rule $(a, b) ϵ R_{1} \Leftrightarrow 1 + a b > 0.$

Prove that : $(a, b) ϵ R_{1}$ and $(b, c) ϵ R_{1}$

$\Rightarrow (a, c) ϵ R_{1}$ is not true for all $a, b c ϵ R$

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