# What Is the Highest Temperature Reached in the Ideal Gas Cycle?

• weinbergshaun
In summary, for the given PV diagram with 7.5 moles of ideal diatomic gas through cycle a, b, and c, the highest temperature reached by the gas is 208°C. The correct calculation should use 30 kPa for pressure (not 3 kPa) and convert the given volume from m^3 to L. The gas constant R can be used in different units, such as 8.31 Pa m^3/(K mol) or 8.31 kPa L/(K mol).
weinbergshaun
Question (see attached diagram):
PV diagram with 7.5 moles of ideal diatomic gas through cycle a, b and c. What is the highest temperature reached by the gas during the cycle? (multiple choice answers 180, 325, 208 and 100 C, i know answer is 208 C but I'm not getting it!) It is a PV diagram with (triangle), pressure is measured in p(PA x 10^4) and volume is V(m^3) The question is on pg 16 at https://www.scribd.com/doc/287176891:
Point a => p = 3 p(PA x 10^4) and v = 0.2 V(m^3)
Point b => p = 5 p(PA x 10^4) and v = 0.6 V(m^3)
Point c => p = 3 p(PA x 10^4) and v = 0.6 V(m^3)

Attempt at question:
Point a:
p = 3 PA x 10^4 (im keeping this and will use R = 8.31 L.KPA/K.mol I THINK PA x 10^4 = kPA!)
V = 600 Litres (converted cubic metres to litres times by 1000)
n = 7,5 (this is given even though its diatomic, it will remain as 7,5 since its moles and not molar mass?
R = 8.31 L.KPA/K.mol T = ? PV = nRT T = PV/Rn T = 3 x 600/8.31 x 7,5

Using T = nR/PV:
T = 1800/62.32 T = 28.8 Kelvin

If i apply this to all the other points then i get nowhere near the 208 C, so this example above shows that one of my values is wrong (and will be wrong for all other points b and c).

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weinbergshaun said:
Question (see attached diagram):
PV diagram with 7.5 moles of ideal diatomic gas through cycle a, b and c. What is the highest temperature reached by the gas during the cycle? (multiple choice answers 180, 325, 208 and 100 C, i know answer is 208 C but I'm not getting it!) It is a PV diagram with (triangle), pressure is measured in p(PA x 10^4) and volume is V(m^3)
Attempt at question:
Point a:
p = 3 PA x 10^4 (im keeping this and will use R = 8.31 L.KPA/K.mol I THINK PA x 10^4 = kPA!)

No, "kilo" means 1000. 3 x 104 Pa=30 kPa.
Why do you use liters and kPa-s when the volume is given in m3-s and the pressure in pascals? And R=8.31 m3 Pa/(K mol) .
And the problem asks the temperature in °C.

weinbergshaun
ehild said:

No, "kilo" means 1000. 3 x 104 Pa=30 kPa.
Why do you use liters and kPa-s when the volume is given in m3-s and the pressure in pascals? And R=8.31 m3 Pa/(K mol) .
And the problem asks the temperature in °C.
Thanks for your assistance. I'm doing the best to figure this out, my books does not give me the laws clearly. So your saying 3 x 10^4 Pa=30 kPa, i was using 3 kPA. I converted cubic meters to liters as i assumed that if you work with pascals you needed to convert the cubic meters to liters and if you work with atmospheric pressure (atm) you work with cubic meters. I also assumed that if you use the kilopascal then you must use R=8.31 and if you just use pascals its the other R = 0,0821 value.

weinbergshaun said:
Thanks for your assistance. I'm doing the best to figure this out, my books does not give me the laws clearly. So your saying 3 x 10^4 Pa=30 kPa, i was using 3 kPA. I converted cubic meters to liters as i assumed that if you work with pascals you needed to convert the cubic meters to liters and if you work with atmospheric pressure (atm) you work with cubic meters. I also assumed that if you use the kilopascal then you must use R=8.31 and if you just use pascals its the other R = 0,0821 value.
3 x 10^4 Pa=30 kPa, using 3 kPa instead is wrong.
R can be used in different units. See
https://en.wikipedia.org/wiki/Gas_constant.
R=8.31 Pa m3/ (K mol) or R=8.31 kPa L / (K mol) .

weinbergshaun
weinbergshaun said:
Thanks for your assistance. I'm doing the best to figure this out, my books does not give me the laws clearly. So your saying 3 x 10^4 Pa=30 kPa, i was using 3 kPA. I converted cubic meters to liters as i assumed that if you work with pascals you needed to convert the cubic meters to liters and if you work with atmospheric pressure (atm) you work with cubic meters. I also assumed that if you use the kilopascal then you must use R=8.31 and if you just use pascals its the other R = 0,0821 value.
Ok got it, thanks this helps ten millions times i think i can finish the question now~

## 1. What are the Ideal Gas Laws?

The Ideal Gas Laws refer to a set of mathematical equations that describe the behavior of an ideal gas under various conditions, such as temperature, pressure, and volume. These laws were developed by scientists to understand and predict the properties and behavior of gases.

## 2. What are the main assumptions of the Ideal Gas Laws?

The Ideal Gas Laws assume that the gas particles have no volume, there are no intermolecular forces between the particles, and the collisions between particles and with the container walls are perfectly elastic. It also assumes that the gas is in a closed system and the temperature is constant.

## 3. How are the Ideal Gas Laws used in real-life applications?

The Ideal Gas Laws are used in various real-life applications, such as in the design and operation of gas-powered engines, refrigeration systems, and weather forecasting. They are also used in the study of the atmosphere, chemical reactions, and industrial processes.

## 4. What is the relationship between temperature and pressure in the Ideal Gas Laws?

According to the Ideal Gas Laws, there is an inverse relationship between temperature and pressure. This means that as the temperature of a gas increases, the pressure also increases and vice versa, as long as the volume and the number of gas particles remain constant.

## 5. What are the units of measurement used in the Ideal Gas Laws?

The units of measurement used in the Ideal Gas Laws are Kelvin (K) for temperature, atmospheres (atm) for pressure, and liters (L) for volume. However, other units such as Celsius (°C), Pascal (Pa), and cubic meters (m3) can also be used as long as they are consistent throughout the equation.

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