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Two identical cylinders with a movable piston contain 0.7 mol of helium gas at a temperature of 300 K. The temperature of the gas in the first cylinder is increased to 564 K at constant volume by doing work W1 and transferring energy Q1 by heat. The temperature of the gas in the second cylinder is increased to 564 K at constant pressure by doing work W2 while transferring energy Q2 by heat.
A. Find Ī”Eint, 1, Q1, and W1 for the process at constant volume.
B. Find Ī”Eint, 2, Q2, and W2 for the process at constant pressure.

Respuesta :

Answer:

Explanation:

A ) At constant volume :

Ī”Eint = n Cv x Ī”T , n is no of moles , Cv is specific heat at constant volume , Ī”T is increase in temperature .

For helium Cv = 3/2 R = 1.5 x 8.3 J = 12.45 J

Ī”Eint = .7 x 12.45 x ( 564 - 300 )

= 2300.76 J .

Wā‚ = 0 because volume is constant so work done by gas is zero .

Qā‚ = Ī”Eint = 2300.76 J

B )

At constant pressure

Qā‚‚ = n Cp Ī” T , Cp is specific heat at constant pressure .

For monoatomic gas ,

Cp = 5/2 R = 2.5 x 8.3 J = 20.75 J

Qā‚‚ = .7 x 20.75 x 264 J

= 3834.6 J

Wā‚‚ = work done by gas

= PĪ”V = nRĪ”T

= .8 Ā x 8.3 x 264

= 1752.96 J

Ī”Eint = Qā‚‚ - Wā‚‚

= 3834.6 - 1752.96

= 2081.64 J.

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Ā Ī”Eint, 1, Q1, and W1 for the process at constant volume. and Ī”Eint, 2, Q2, and W2 for the process at constant pressure is mathematically given as

a)

dE1= 2300.76 J .

W1=0 as Volume is constant

Q1= 2300.76 J as Q= dE1

b)

Q2= 3834.6 J

W2= 1752.96 J

dE2= 2081.64 J. Ā 

What is Ī”Eint, Q1 and W1 for the process at constant volume and pressure?

a)

Generally, the equation for the Constant Volume Ā Ā is mathematically given as

dE = n Cv x dT

Where

Cv = 3/2

R = 1.5 x 8.3 J

R= 12.45 J

Therefore

dE = 0.7 x 12.45 x ( 564 - 300 )

dE1= 2300.76 J .

W1=0 as Volume is constant

Q1= 2300.76 J as Q= dE1

b)

Generally

Q2 = n Cp dT

Where

Cp = 5/2

R = 2.5 x 8.3 J

R= 20.75 J

Hemce

Q2 = 0.7 x 20.75 x 264 J

Q2= 3834.6 J

For Work done

W=PdV

W= nRdT

Therefore

W= 0.8 Ā x 8.3 x 264

W2= 1752.96 J

Hence

dE = Qā‚‚ - Wā‚‚

dE= 3834.6 - 1752.96

dE2= 2081.64 J. Ā 

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