According to the Ideal Gas Law,PV = kT,where P is pressure, V is volume, T is temperature (in kelvins), and k is a constant of proportionality. A tank contains 2600 cubic inches of nitrogen at a pressure of 20 pounds per square inch and a temperature of 300 K.(a) Determine k.k = (b) Write P as a function of V and T and describe the level curves.P =Setting P = c, the level curves are of the formV =

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preety89 preety89 · Answer 1 · 2020-03-14T13:09:39+01:00

Answer:

The value of k = 173.34

Step-by-step explanation:

(a). Pressure ( P )= 20 [tex]\frac{lb}{in^{2} }[/tex]

Volume ( V ) = 2600 [tex]in^{3}[/tex]

Temperature ( T ) = 300 K

From the Ideal Gas Law, P V = k T -------------(1)

⇒ k = [tex]\frac{P V }{T}[/tex]

Put all the values in the above formula we get

⇒ k = [tex]\frac{20}{300}[/tex] × 2600

⇒ k = 173.34

This is the value of k.

(b). From the Ideal Gas Law, P V = k T

⇒ P = k ×[tex]\frac{V}{T}[/tex]

⇒ P = function of [tex]\frac{V}{T}[/tex] -------------- (2)

⇒ P is directly proportional to [tex]\frac{V}{T}[/tex]

The curve between P & [tex]\frac{V}{T}[/tex] is as follows.

shristiparmar1221 shristiparmar1221 · Answer 2 · 2022-01-01T09:35:35+01:00

i.) The value of k is 173.3334.

ii.) The curve between pressure and Time/Volume(T/V) will be constant.

Given to us:

Pressure P = 20 pounds/inch²,

Volume V = 2600 inch³,

Temperature T = 300 K,

Ideal Gas Law Equation, PV = kT

a.) To find out the value of k,

[tex]PV = kT\\20\times 2600 = k\times 300\\\\k = \dfrac{20\times 2600}{300}\\\\k= 173.3334[/tex]

Therefore, the value of k is 173.3334.

b.) Curve of P as a function of V and T,

[tex]PV=kT\\\\P=k\frac{T}{V}\\\\\dfrac{P}{\frac{T}{V}} = k=constant[/tex]

Therefore, the curve between pressure and Time/Volume(T/V) will be constant.

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