Question

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.

Answer 1

A)

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

V_i = initial volume = 0.033 m³

T_i = initial temperature = ?

n = number of moles = 3

Using the equation

PV_i = nRT_i

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

T_i = 389 K

b)

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

V_f = final volume = 0.045 m³

T_f = initial temperature = ?

n = number of moles = 3

Using the equation

PV_f = nRT_f

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

T_f = 530.4 K

C)

work done is given as

W = P (V_f - V_i) = (2.94 x 10⁵) ((0.045) - (0.033)) = 3528 J

d)

Q = n C_p (T_f - T_i) = (3) (2.5) (8.314) (530.4 - 389) = 8817 J

e)

Using first law

Q = W + U

8817 = 3528 + U

U = 5289 J