A gas has an initial volume of 1.00 m³.It is expanded to five times its original volume through a quasi-static process for which P = a V ⁴,with a = 3.00 N/m¹⁴.How much work is done by the expanding gas?

Question

Quizplus · Accepted Answer

The work done by the expanding gas can be calculated using the formula:

W = ∫ P dV

Since the process is quasi-static, we can use the equation of state to express pressure in terms of volume:

P = a V^(1/4)

Substituting this into the expression for work, we get:

W = ∫ a V^(1/4) dV

Integrating this with limits from V_i = 1.00 m^3 to V_f = 5.00 m^3, we get:

W = (4/5) a (V_f^(5/4) - V_i^(5/4))

Substituting the given values of a and V_i and simplifying, we get:

W = 1.87 kJ

Therefore, the best choice is C.

A Gas Has an Initial Volume of 1