Question

For the following process, use a calculation to predict whether or not it will occur spontaneously.

A piston with radius of 10.0 cm containing 4.00 L of an ideal gas (Cv,m = 3/2 R) at 1.03 atm, 298.15 K undergoes isothermal expansion when a 4.63 kg weight that was sitting on the piston was quickly removed.

Answer 1

Given:- The radius of the base of the piston, r = 10.0 cm

Also, 1 cm = 0.01 m

So, r = 0.1 m

The area of the base of the piston, A can be calculated as:-

So,

The force acting due to the weight is:-

So, Force, F can be calculated as:-

The pressure due to this weight can be calculated as:-

The expression for the conversion of pressure in Pascal to pressure in atm is shown below:

Given the value of pressure = 1445.1257 Pa

So,

Pressure = 0.01426 atm

Given, Atmospheric pressure=1.03 atm

So, Initial pressure = 1.03 + 0.01426 atm = 1.04426 atm

The weight is removed.

So, Final pressure = 1.03 atm

Also,

Using ideal gas equation as:

where,

P is the pressure = 1.04426 atm

V is the volume = 4.00 L

n is the number of moles

T is the temperature = 298.15 K

R is Gas constant having value = 0.0821 L.atm/K.mol

Applying the equation as:

1.04426 atm × 4.00 L = n × 0.0821 L.atm/K.mol × 298.15 K

⇒n = 0.1706 moles

The expression for the calculation of entropy change for isothermal expansion of the ideal gas is:-

Where, R is the gas constant (8.314 J /mol K)

So,

Also,

The expression for the standard change in free energy is:

Where,

is the change in the Gibbs free energy.

T is the absolute temperature. (T in kelvins)

is the enthalpy change of the reaction.

is the change in entropy.

For isothermal expansion of an ideal gas,

So,

Also, For a system to be spontaneous,

Thus, must be positive for the system to be spontaneous.

(Positive) and thus, the system is spontaneous.