1 mol of an ideal gas with Cp=20J/K/mol is maintained at 400k in a volume of 50dm^3. Determine the initial pressure of the system if the gas is heated reversibly to 500K at constant pressure

Answer 1

To determine the initial pressure of the system, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure
V = volume (converted to m^3)
n = number of moles
R = ideal gas constant = 8.314 J/mol∙K
T = temperature (converted to K)

Given:
Cp = 20 J/K/mol
Initial temperature (T1) = 400 K
Final temperature (T2) = 500 K
Volume (V) = 50 dm^3 = 0.05 m^3

First, we need to calculate the number of moles (n) using the specific heat capacity (Cp) provided.

Cp = (5/2)R
20 = (5/2) * 8.314
20 = 10.39

n = Cp / (5/2)R
n = 10.39 / (5/2 * 8.314)
n = 0.499 mol

Now, let's calculate the initial pressure (P1) using the ideal gas law:

P1 * V = n * R * T1
P1 = n * R * T1 / V
P1 = 0.499 * 8.314 * 400 / 0.05
P1 = 7981.79 Pa

Therefore, the initial pressure of the system is 7981.79 Pa.