Question

A vessel of 25 litres capacity contains 10 moles of steam under pressure of 50.3atm calculate the temperature of steam using vandervaals equation

Answer 1

temperature of steam using Van Dar Waals equation is 1541 K.

Given : A vessel of 25 litres capacity contains 10 moles of steam under pressure of 50.3 atm.

a= 5.46 bar L² mol¯² and b = 0.031 mol¯1.

To find : The temperature of steam using Van Dar Waals equation .

solution : Using gaseous formula for real gas,

$\left(P+\frac{an^2}{V^2}\right)(V-nb)=nRT$

here, P = 50.3 atm

V = 25 L

n = 10

a = 5.46 bar L² mol¯²

b = 0.031 mol¯¹

[50.3 + (5.46 × 10²)/25²][25 - 10 × 0.031] = 10 × 0.082 × T

⇒[50.3 + 546/625] [25 - 0.31] = 0.82T

⇒(50.3 + 0.8736)(24.69) = 0.82T

⇒(51.1736)(24.69) = 0.82T

⇒T = 1540.82461 ≈ 1541 K

Therefore temperature of steam using Van Dar Waals equation is 1541 K