Question

Two moles of gas are confined in a piston–cylinder device. Initially, the temperature is at 300 K and the pressure is 1 bar. The gas is compressed isothermally to 5 bar. If the ideal gas heat capacity is C ig P = 7R/2, find Q, W, ?U, ?H, and ?S if:

(a) the gas is ideal, or

(b) the gas satisfies the van der Waals equation of state with a = 5.0 × 106 bar · cm6/mol2 and b = 30 cm3/mol.

(c) Comment on the differences

Answer 1

Given:

2 moles of a gas

T₁= 300 K

P₁= 1 bar

P₂= 5 bar

C_ig= 7R/2

• As given process is an isothermal compression process

  

  As they are the function of temperature

(a)

As is zero,

It is given that gas behaves Ideally

Calculate   and     by using above equation

use   

For an isothermal process work is calculated as,

(b)

Gas satisfies van der Waals equation of state given by

Calculate   and   by using above equation

Similarly,

Now, calculate work by using formula

putting respective values in above equation we get,

(c)

from above calculation, it is evident that considering gas as ideal may lead to giving work or heat more by just 1%

which is a negligible error