Question

A cylinder containing three moles of nitrogen gas is heated at a constant pressure of 2 atm. The temperature of the gas changes from 300 K to 350 K as a result of the expansion. Find work done

(a) on the gas, and
(b) by the gas by using van der Waals equation of state instead of ideal gas law.

Answer 1

To find the work done by the gas using the van der Waals equation of state, calculate the change in volume and use the formula for work done on a gas at constant pressure. To find the work done by the gas, calculate the integral of P dV using the van der Waals equation of state.

Step-by-step explanation:

In order to find the work done by the gas using the van der Waals equation of state, we first need to calculate the change in volume. To find the work done by the gas using the van der Waals equation of state, calculate the change in volume and use the formula for work done on a gas at constant pressure. To find the work done by the gas, calculate the integral of P dV using the van der Waals equation of state.

ΔV = V₂ - V₁ = R x T₁ x [(P₂ + a/V₂)(V₂ - b) - (P₁ + a/V₁)(V₁ - b)] / [(P₂ + a/V₂) - (P₁ + a/V₁)]

Once we have the change in volume, we can use the formula for work done on a gas at constant pressure: W = P x ΔV.

For the work done by the gas, we need to calculate the integral of P dV from V₁ to V₂, which can be evaluated using the van der Waals equation of state.