Gas expansion and such

In summary, the pressure of a gas inside a cylinder can be calculated using the ideal gas law, which states that PV = nRT.
  • #1
Jeffopolis
12
0
Suppose 1.2 mol of a monatomic ideal gas initially at 11 L and 300 K is heated at constant volume to 590 K, allowed to expand isothermally to its initial pressure, and finally compressed at constant pressure to its original volume, pressure, and temperature. During the cycle, what are (a) the net energy entering the system (the gas) as heat and (b) the net work done by the gas? (c) What is the efficiency of the cycle?

ok so here's what i got, (Ta, Va, refer to point a's temp, volume, etc) did some work and i figured these numbers out

Pa= .40625atm = 41163.28 Pa
Va= .0042 cubic meters
Ta= 21 Kelvin
Pb= 13atm = 1317225 Pa
Vb= .0042 cubic meters
Tb= 666 Kelvin
Pc= .40625 atm = 41163.28 Pa
Vc= .0336 cubic meters
Tc= 166 Kelvin

Now, I am not sure if I am using the right formulas?

DeltaE (internal energy) = (3/2)nRT ?
Q = nC DeltaT ?
W = nC DeltaT ?

I'm not sure if i wrote them wrong in my notes or something, but is this not how you get the heat, work, energy for each transition?

And then, after the full cycle, DeltaE should = 0 correct?Also, i need to get this answered asap as i have a lab writeup due tomorrow... given volume, diameter of a cylinder, initial room pressure, how do you find the pressure of a gas inside said cylinder?
 
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  • #2
To find the pressure of a gas inside a cylinder, you need to use the ideal gas law. The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles of the gas, R is the ideal gas constant, and T is temperature. You can rearrange this equation to solve for P, giving P = (nRT)/V. So, if you know the volume, number of moles, temperature, and ideal gas constant, you can calculate the pressure of the gas inside the cylinder.
 

1. What is gas expansion?

Gas expansion is the process by which a gas increases in volume when its pressure is reduced or its temperature is increased. This results in the gas molecules spreading out and taking up more space.

2. What causes gas expansion?

The main factors that cause gas expansion are changes in pressure and temperature. When the pressure on a gas is decreased, the gas molecules have more space to move around and thus expand. Similarly, increasing the temperature of a gas causes its molecules to move faster and take up more space, leading to expansion.

3. How does gas expansion affect its surroundings?

Gas expansion can have various effects on its surroundings. In enclosed spaces, it can increase the pressure and potentially cause explosions. In open spaces, it can cause winds and other atmospheric phenomena. It can also have an impact on the temperature and humidity of the surrounding environment.

4. What is the ideal gas law and how does it relate to gas expansion?

The ideal gas law is a mathematical equation that describes the relationship between the 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 temperature and number of moles of the gas. This law helps us understand and predict how gases will behave during expansion.

5. How is gas expansion used in everyday life?

Gas expansion is used in many everyday applications, such as in air conditioning and refrigeration systems. It is also the principle behind hot air balloons and other forms of transportation that use gas expansion to generate lift. Additionally, gas expansion is important in the production of various goods, such as aerosol cans, where the expanding gas helps to propel the product out of the container.

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