Question

# Three moles of an ideal monatomic gas expand at a constant pressure of 2.90atm : the...

Three moles of an ideal monatomic gas expand at a constant pressure of 2.90atm : the volume of the gas changes from 3.30*10^-2m^3 to 4.50*10^-2m^3.

Part A, Calculate the initial temperature of the gas.

Part B, Calculate the final temperature of the gas.

Part C, Calculate the amount of work the gas does in expanding.

Part D, Calculate the amount of heat added to the gas.

Part E, Calculate the change in internal energy of the gas.

A)

P = pressure = 2.90 atm = 2.90 x 1.01 x 105 Pa = 2.94 x 105 Pa

Vi = initial volume = 0.033 m3

Ti = initial temperature = ?

n = number of moles = 3

Using the equation

PVi = nRTi

(2.94 x 105) (0.033) = (3) (8.314) Ti

Ti = 389 K

b)

P = pressure = 2.90 atm = 2.90 x 1.01 x 105 Pa = 2.94 x 105 Pa

Vf = final volume = 0.045 m3

Tf = initial temperature = ?

n = number of moles = 3

Using the equation

PVf = nRTf

(2.94 x 105) (0.045) = (3) (8.314) Tf

Tf = 530.4 K

C)

work done is given as

W = P (Vf - Vi) = (2.94 x 105) ((0.045) - (0.033)) = 3528 J

d)

Q = n Cp (Tf - Ti) = (3) (2.5) (8.314) (530.4 - 389) = 8817 J

e)

Using first law

Q = W + U

8817 = 3528 + U

U = 5289 J