Calculating Heat Added/Removed to Ideal Gas System

• mikefitz
In summary: For constant pressure the work is: W = P\Delta V For the problem, increasing the pressure increased the work done by the system.
mikefitz

Homework Statement

A monatomic, ideal gas is in a sealed container (the number of gas molecules is always constant: n = 2 moles); the initial pressure is Pi = 1.01 x 10^5 Pa and the initial volume is Vi = 0.0224 m^3.

* First, the volume of the gas is decreased at a constant pressure (at Pi = 1.01 x 10^5 Pa) to a final volume of Vf = 0.0155 m^3.
* Second, the pressure of the gas is increased at a constant volume (at Vf = 0.0155 m3) to a final pressure of Pf = 1.35 x 10^5 Pa.

How much heat was added to (give as a positive number) or removed from (give as a negative number) the system? (The gas constant R = 8.31 J/mole-K.)

PV = nRT

The Attempt at a Solution

I guess I am confused as to how I am supposed to solve this problem without knowing the heat capacity or the specific heat of the substance.

I have calculated Ti=94.14 and Tf=125.83 - deltaT=31.692 C - why is this incorrect?

The heat capacity at constant volume of an ideal gas is: $$c_{v}NR$$.

$$c_{v} = \frac{3}{2}$$ for a monatomic gas, and $$\frac{5}{2}$$ for a diatomic gas.

The heat capacity at constant pressure of an ideal gas is:

$$(c_{v}+1})NR$$

Problem Solved.

Please look at case one of the pressure vs volume graph:

http://img99.imageshack.us/img99/2964/followuphz6.gif

I thought to get the total work done by the system I would take the work done by decreasing volume and add the work done by increasing pressure.

To get the total work done all I had to do was use the work done by the system decreasing volume. (-696.9J)

Why didn't I have to add on the work done by the increase in pressure? I calculated that to be 527J, where does this energy disappear to?

thanks

Last edited by a moderator:
The work done is the area under the graph of pressure versus volume. When you increase the volume, the gas does positive work.

$$W = P\Delta V$$

For non-constant pressure the work is:

$$W = \int_{V_{1}}^{V_{2}} P\; dV$$

Last edited:

What is the definition of ideal gas?

An ideal gas is a theoretical gas composed of particles that have negligible volume and do not interact with each other. This means that the gas behaves according to the ideal gas law, which relates the pressure, volume, and temperature of the gas.

How do you calculate the heat added/removed to an ideal gas system?

The heat added/removed to an ideal gas system is calculated using the formula Q = nCvΔT, where Q is the heat added/removed, n is the number of moles of gas, Cv is the specific heat capacity at constant volume, and ΔT is the change in temperature.

What is the specific heat capacity at constant volume?

The specific heat capacity at constant volume, Cv, is the amount of heat required to raise the temperature of one mole of an ideal gas by 1 degree Celsius when the volume is kept constant.

How does the heat added/removed affect the temperature of an ideal gas system?

The heat added/removed to an ideal gas system causes a change in temperature according to the equation Q = nCvΔT. This means that the temperature will increase if heat is added and decrease if heat is removed.

What are some real-life applications of calculating heat added/removed to ideal gas systems?

Calculating heat added/removed to ideal gas systems is important in many industrial processes, such as in refrigeration and air conditioning systems. It is also used in the study of thermodynamics, which has applications in fields such as engineering, physics, and chemistry.

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