A Fixed Amount of Ideal Gas Goes Through a Process

question 96

Essay

A fixed amount of ideal gas goes through a process abc. In state a, the temperature of the gas is 152°C, its pressure is 1.25 atm, and it occupies a volume of 0.250 m³. It then undergoes an isothermal expansion to state b that doubles its volume, followed by an isobaric compression back to its original volume at state c. (Hint: First show this process on a pV diagram.) The ideal gas constant is 8.314 J/mol ∙ K, and 1.00 atm = 1.01 × 10⁵ Pa.
(a) How many moles does this gas contain?
(b) What is the change in the internal energy of the gas between states a and b?
(c) What is the net work done on (or by) this gas during the entire process?
(d) What is the temperature of the gas in state c?

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Definitions:

Short Run

In economics, a period during which at least one of a firm's inputs is fixed and cannot be changed.

Fixed Input

An input in the production process that cannot be changed in the short term, such as buildings or land.

Long-Run Adjustment

A process in which firms adjust their inputs and outputs to achieve the optimal level of production and efficiency over an extended period.

Farmer

An individual engaged in the activity of agriculture, aiming to produce crops and raise livestock for consumption or sale.