Thermodynamics Ideal Gas Problem

In summary, the ideal gas expands along a straight diagonal path from (p_1, V_1) to (p_2, V_2), where p_2 = 2p_1 and V_2 = 2V_1. The work done by the gas during this process can be expressed as W = (p_1 V_1 - p_2 V_2) / (y - 1), with y = 1.4. However, instead of trying to apply an equation, it is recommended to use theory and common sense to calculate the area under the straight line on a pressure vs volume plot to determine the work.
  • #1
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Homework Statement


An ideal gas expands from the state (p_1, V_1 ) to the state (p_2, V_2 ), where p_2 = 2p_1 and V_2 = 2V_1. The expansion proceeds along the straight diagonal path AB shown in the figure.

Find an expression for the work done by the gas during this process.
Express your answer in terms of the variables p_1 and V_1.


Homework Equations


W = (p_1 V_1 - p_2 V_2) / (y - 1)

The Attempt at a Solution


I put the equation exactly with y = 1.4.
Masteringphysics says "Your answer either contains an incorrect numerical multiplier or is missing one.".

What have I done wrong?
 
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  • #2
Is that an equation from a textbook? Don't think about trying to apply an equation. Instead, use theory and some common sense.

You state in the problem that there is a figure that you don't show. It does sound like you have a pressure vs volume plot where there is a straight line from p1,V1 to p2,V2.

With that, work is basically the area under that line. Calculate that area for work.
 
  • #3
I have managed to solve this problem. Thank you.
 

FAQ: Thermodynamics Ideal Gas Problem

What is the Ideal Gas Law and how is it related to Thermodynamics?

The Ideal Gas Law is a fundamental law in thermodynamics that describes the relationship between pressure, volume, temperature, and number of moles of an ideal gas. It states that the product of pressure and volume is directly proportional to the absolute temperature and the number of moles of the gas. This law is derived from the principles of thermodynamics and is used to predict the behavior of ideal gases at different temperatures and pressures.

What is an ideal gas and how does it differ from a real gas?

An ideal gas is a hypothetical gas that follows the Ideal Gas Law at all temperatures and pressures. It is composed of point particles that have no volume and do not interact with each other. On the other hand, real gases have non-negligible volumes and do interact with each other, which results in deviations from the Ideal Gas Law at high pressures and low temperatures.

What are the assumptions made in solving an Ideal Gas Problem?

To solve an Ideal Gas Problem, the following assumptions are made: the gas is considered to be an ideal gas, the gas is in a closed system with constant temperature and number of moles, and the gas particles do not interact with each other. Additionally, the Ideal Gas Law assumes that the volume occupied by the gas particles is negligible compared to the volume of the container.

How do you calculate the number of moles of an ideal gas?

The number of moles of an ideal gas can be calculated using the Ideal Gas Law. The equation is n = PV/RT, where n is the number of moles, P is the pressure, V is the volume, R is the gas constant, and T is the absolute temperature. This equation can also be rearranged to solve for any of the other variables, depending on the information given in the problem.

What is the difference between isothermal, isobaric, and isochoric processes in thermodynamics?

An isothermal process is one in which the temperature of the gas remains constant, while the pressure and volume may vary. An isobaric process is one in which the pressure of the gas remains constant, while the temperature and volume may vary. An isochoric process is one in which the volume of the gas remains constant, while the temperature and pressure may vary. These processes are important in understanding the behavior of ideal gases and are often used to analyze thermodynamic systems.

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