First slide

Different type of processes

Question

Figure shows the adiabatic curve for n moles of an ideal gas; the bulk's modulus for the gas corresponding to the point P will be

Difficult

A

$nR (1 + \frac{2 T_{0}}{V_{0}})$
B

$nR (2 + \frac{T_{0}}{V_{0}})$
C

$nR (1 + \frac{T_{0}}{V_{0}})$
D

$nR (1 + \frac{T_{0}}{2 V_{0}})$

Solution

Bulk's modulus K = $\frac{- dP}{\frac{dV}{V}} = γP [{PV}^{γ} = constant]$
For the curve ${TV}^{γ - 1} = k (constant)$
or $V dT + T (γ - 1) dV = 0$
or $\frac{dV}{dT} = \frac{- V}{(γ - 1) T} = - 1 (slope at point P)$
$∴ γ = 1 + \frac{V_{0}}{T_{0}}$
$∴ K = γ [\frac{{nRT}_{0}}{V_{0}}] = nR (1 + \frac{T_{0}}{V_{0}})$

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