pr4ever

17.10.2019 •

Mathematics

Use the rules for operations with integers to simplify the expression.

-8 - -2

a. -10

b. -6

c. +6

d. +10

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Ответ:

Dee1738

25.10.2020

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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Use the rules for operations with integers to simplify the expression. -8 - -2 a. -10 b. -6 c. +6 d. +10

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Use the rules for operations with integers to simplify the expression.

-8 - -2

a. -10

b. -6

c. +6

d. +10