Question

NOTE: The problems are all subparts of each other. I noted the numbers I was able to find in parenthesis. I just need help with the bolded questions.

Suppose 2 moles of a monatomic ideal gas occupies 5 m^3 at a pressure of 1600 Pa. Find the temperature of the gas in Kelvin? (I found it 481 K) Find the total internal energy of the gas? (I found it 12000 J ). Suppose the gas sundergoes an isobaric expansion to a volume of 7 m^3. Find Q? Find W? (I got -3200 J) Find U? (I got 4800 J). Suppose the gas then undergoes adiabatic expansion to a pressure of 900 Pa and a volume of 11.5 m³. Find W? Find ?U? The gas then undergoes isothermal compression to a volume of 5 m³. Find Q? Find W? The gas then undergoes an isochoric process and returns to 1600 Pa of pressure. Find Q? Find ?U ?

Answer 1

(A) P V = n R T

(1600) (5) = (2)(8.314)(T)

T = 481 K  

(B) U = 3 n R T / 2 OR 3 P V / 2

= (1.5)(1600)(5)

= 12000 J

--------------------------

For isobaric,

W = P deltaV = 1600 x (7 - 5) = 3200 J ....Ans

Q = n Cp deltaT = (5/2)(n R deltaT ) = (2.5) P deltaV  

Q = 8000 J .....And

delta(U) = Q - W = 8000 - 3200 = 4800 J  

Uf - Ui = 4800

U = (4800) + 12000 = 16800 J .....Ams

----------------------------------

Adiabatic:

W = (900)(11.5)^(5/3) [ 11.5^(--2/3) - 7^(-2/3)] / (-2/3)

W = 6090 J .....Ans

deltaU = -W =- 6090 J .....Ans

-----------------------

Isothermal:

W = P V ln(VF/Vi) = (900 x 11.5) ln(5/11.5)

W = - 8620 J ....Ans

Q = W = - 8620 J .....Ans

----------------------

Isochoric:

Q = deltaU = n Cv deltaT = (3/2)(n R deltaT)

= (3/2) V deltaP

= (3/2) (5)(1600 - 2070)

= - 3525 J ....Ans