If gas in a cylinder is maintained at a constant

Ответ:

Dee1738

22.01.2022

Mathematics

(a) $\frac{dP}{dV}=\frac{2an^2}{V^3}-\frac{nRT}{(V-nb)^2}$

(b) $\frac{dP}{dt}=\frac{nR(V-nb)\frac{dT}{dt}-nRT\frac{dV}{dt}}{(V-nb)^2}+\frac{2an^2\frac{dV}{dt}}{V^3}$

$\frac{dP}{dt}$ is the rate change of pressure of the gas per unit time.

Step-by-step explanation:

Formula:

$\frac{d}{dx}(\frac uv)=\frac {v\frac{d}{dx}v-u\frac{d}{dx}v}{v^2}$

Given that,

$P=\frac{nRT}{V-nb}-\frac{an^2}{V^2}$

(a)

$P=\frac{nRT}{V-nb}-\frac{an^2}{V^2}$

Differentiating with respect to V

$\frac{dP}{dV}=\frac{(V-nb)\frac{d}{dV}(nRT)-(nRT)\frac{d}{dV}(V-nb)}{(V-nb)^2}-\frac{V^2\frac{d}{dV}(an^2)-(an^2)\frac{d}{dV}V^2}{(V^2)^2}$

$=\frac {-nRT}{(V-nb)^2}-\frac{-an^2. 2V}{V^4}$

$=\frac{2an^2}{V^3}-\frac{nRT}{(V-nb)^2}$

(b)

$P=\frac{nRT}{V-nb}-\frac{an^2}{V^2}$

Differentiating with respect to t

$\frac{dP}{dt}=\frac{(V-nb)\frac{d}{dt}(nRT)-(nRT)\frac{d}{dt}(V-nb)}{(V-nb)^2}-\frac{V^2\frac{d}{dt}(an^2)-(an^2)\frac{d}{dt}V^2}{(V^2)^2}$

$=\frac{(V-nb)nR\frac{dT}{dt}-nRT\frac{dV}{dt}}{(V-nb)^2}-\frac{-an^2.2V\frac{dV}{dt}}{V^4}$

$=\frac{nR(V-nb)\frac{dT}{dt}-nRT\frac{dV}{dt}}{(V-nb)^2}+\frac{2an^2\frac{dV}{dt}}{V^3}$

(c)

$\frac{dP}{dV}$ is the rate change of pressure of the gas per unit volume.

$\frac{dP}{dt}$ is the rate change of pressure of the gas per unit time.

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Ответ:

isabeljackson562

10.07.2020

Mathematics

This function is odd

Step-by-step explanation:

In order to find if a function is even or odd, you have to start by plugging -x in for x. If the function is exactly the same, then it is even. If it is opposite, then it is odd. This will produce an opposite function thus making it odd.

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