Question

for a given amount of ideal gas, if A. be the slope of p-V curve for its isothermal process and B be the slope of P-V curve for its adiabatic process then gamma =cp/c v equals​

Answer 1

Answer:

The adiabatic constant of the process is given as

$\frac{B}{A} = \gamma$

Explanation:

For isothermal process we know that process equation is given as

$PV = K$

now the slope of its PV curve is given as

$\frac{dP}{dV} V + P = 0$

$\frac{dP}{dV} = - \frac{P}{V}$

so we have

$A = - \frac{P}{V}$

similarly we know that process equation of adiabatic process is given as

$PV^{\gamma} = K$

now we will have

$\frac{dP}{dV} V^{\gamma} + \gamma PV^{\gamma - 1} = 0$

so we have

$\frac{dP}{dV} = -\gamma\frac{P}{V}$

so we know that

$B = -\gamma\frac{P}{V}$

now divide the above two equations

$\frac{B}{A} = \gamma$

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Topic : Slope of adiabatic process

https://brainly.in/question/6933040

Answer 2

answer is in the attachment given below