Question

Internal energy of a gas obeying van der waals equation depends on

Answer 1

Since the options are not given, I am giving a general answer.

The internal energy of a gas which obeys the Vanderwaal's equation - depends on the specific volume and the temperature.

For a Vanderwaal's gas, the internal energy can be computed from the equation-

(δE / δV) T = T (δP /δT) V – P

But, P = RT / (v-b) – a/v²

(δP / δT) V = R / v - b

(δE / δV) T = T (R / v - b) – [(RT / v - b) – (a / v²) = a / v²

 

 (δE / δV) T = αT Kt - P

 

Kt = -v (δP / δV) T = -v (2a / v³) = -2a / v²

So, (δcV / δV) T = T (δ²P / δT²) = 0

d ∈ = cV (T) dT + (a / v2) dv.