# Thermodynamics help Ideal gas equation

• Noor123
In summary, the homework statement is that the product pV of 1 mol of a dilute gas is 22.98 L atm at 0°C and 31.18 L atm at 100°C. The perfect gas law is valid, with T = t(°C) + a, and the value of R is not known. R and a were determined from the measurements provided.
Noor123

## Homework Statement

Suppose that you measured the product pV of 1 mol of a dilute gas and found
that pV = 22.98 L atm at 0°C and 31.18 L atm at 100°C. Assume that the perfect gas law
is valid, with T = t(°C) + a, and that the value of R is not known.

Determine R and a from the measurements provided. Express your result for R in J K

--------------

PV = nRT
T = t(°C) + a

## The Attempt at a Solution

Ok I answered the first part:
R = slope = (31.18 - 22.98 / 100 - 0 )
= 0.082 L atm C

what is a ??how do I find it??

What temperature scale should be used in the ideal gas equation?

What do you mean?

What temperature scales do you know?

ohh well we usually do it in Kelvin, but the question asks for Celsius, so I guess we don't have to convert anything, no?

How do you convert between C and K? What is "a"?

Note, your R value looks correct, but you are just lucky - "a" canceled out.

C= value of Temp in C + 273.15 = value in K

I have no idea what "a" is.

I don't understand the meaning behind the given equation: T = t(°C) + a

What's t(°C) ? and how are we supposed to use it to determine "a"?

I'm so lost. :(

It is so simpe that you will feel ashamed once you will get it Compare two equations that you have wrote:

temp in K = temp in C + 273.15

T = t(°C) + a

Note, that T means absolute temperature (Kelvins), while t(°C) means temperature in Celsius degrees. Do you see that it is the same equation?

haha ok, so a is 273.15

so you're basically saying,

PV = n R (t(°C) + a)

1) 22.98 = nRa
2) 31.18 = nR(100 + a)

If we do 2-1

31.18 - 22.98 = 100Rn + nRa - nRa
8.20 = 100R (1 mol)
R = 0.0820 L atm C

and if we plug back into one of the equations,
we get 22.98 L atm= (1mol) (0.0820L atm C)a

a = 280.24 C ?
is this our right unit?

## 1. What is the ideal gas equation?

The ideal gas equation, also known as the ideal gas law, is a fundamental equation in thermodynamics that describes the relationship between the pressure, volume, and temperature of an ideal gas. It is written as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature in Kelvin.

## 2. What is the significance of the ideal gas equation?

The ideal gas equation is significant because it provides a simple and accurate way to describe the behavior of gases at different conditions. It helps to predict the change in properties of a gas when pressure, volume, or temperature is varied, and is used in many practical applications, such as in the design of engines and industrial processes.

## 3. How does the ideal gas equation relate to thermodynamics?

The ideal gas equation is based on the principles of thermodynamics, specifically the Ideal Gas Law which states that at a constant temperature, the product of pressure and volume of an ideal gas is proportional to its temperature. This equation is derived from the First Law of Thermodynamics, which states that energy cannot be created or destroyed, but can only be transferred or converted.

## 4. What are the assumptions behind the ideal gas equation?

The ideal gas equation assumes that the gas particles have negligible volume and do not interact with each other. It also assumes that the gas behaves ideally, meaning that it follows the Ideal Gas Law exactly. In reality, no gas is truly ideal, but the ideal gas equation is a good approximation for many gases under certain conditions.

## 5. How can the ideal gas equation be applied in real-life situations?

The ideal gas equation is used in various fields, such as chemistry, physics, and engineering, to calculate and predict the behavior of gases. It is used in the design and operation of engines, refrigerators, and other industrial processes. It is also used in weather forecasting, as changes in atmospheric pressure, volume, and temperature can be described by the ideal gas equation.

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