Did the Pressure of a Monatomic Gas Change During Isentropic Heating?

In summary, the question asks to determine the change in pressure of a monatomic ideal gas when it is heated from 289K to 458K while keeping entropy constant. The initial volume of the sample is provided as 0.0980m^2 and the amount of gas is 3.65 mol. Using the formula for isentropic processes, the volume can be calculated and then substituted into the ideal gas formula. The correct answer is a factor of 3.16, which was initially incorrectly calculated as 0.316 due to a decimal mistake.
  • #1
kolua
69
3

Homework Statement


A sample containing 3.65 mol of a monatomic ideal gas is heated from 289K to 458K, and the entropy remains constant. If the initial volume of the sample was 0.0980m^2, by what factor did the pressure increase or decrease during this process?

Homework Equations

The Attempt at a Solution


it's isentropic. use the formula to get volume and then substitute it into ideal gas formula? would love some hints please!
 

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  • #2
kolua said:
it's isentropic. use the formula to get volume and then substitute it into ideal gas formula?
That should work. What did you get?
 
  • #3
TSny said:
That should work. What did you get?
I got 0.316 and the answer is 3.16. thanks, I think I might have made mistake in the decimal.
 
  • #4
I agree with the answer of 3.16. If you can't find your error, post the details of your work.
 

1. What is the relationship between pressure and volume of gas?

The relationship between pressure and volume of gas is known as Boyle's Law, which states that at a constant temperature, the pressure of a gas is inversely proportional to its volume. This means that as the volume of a gas decreases, the pressure of the gas will increase, and vice versa.

2. How does temperature affect the pressure of a gas?

According to Charles's Law, the pressure of a gas is directly proportional to its temperature when the volume is held constant. This means that as the temperature of a gas increases, the pressure of the gas will also increase, and vice versa.

3. What is the ideal gas law and how does it relate to pressure change?

The ideal gas law, also known as the combined gas law, states that the pressure, volume, and temperature of a gas are all related to each other. This means that any change in pressure, volume, or temperature will affect the other properties. The ideal gas law can be used to predict the pressure change of a gas when other properties are known.

4. How does the amount of gas affect its pressure?

According to Avogadro's Law, the pressure of a gas is directly proportional to the number of moles of gas when the temperature and volume are held constant. This means that increasing the amount of gas will result in an increase in pressure, and decreasing the amount of gas will result in a decrease in pressure.

5. What is the difference between absolute pressure and gauge pressure?

Absolute pressure is the total pressure exerted by a gas, including atmospheric pressure. Gauge pressure, on the other hand, is the pressure measured above atmospheric pressure. This means that absolute pressure is always higher than gauge pressure. Gauge pressure is often used in pressure measurements, while absolute pressure is used in thermodynamic calculations.

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