Ideal gas equation and heat problem

In summary, the conversation discusses the change in volume of an ideal gas from state 1 to state 2, based on a given P-T diagram. The speaker uses the ideal gas equation to show that the volume should remain constant, but the book's answer states that the volume increases. The expert concludes that the volume will indeed stay constant since the P-T graph is a straight line.
  • #1
Amith2006
427
2
Sir,
An ideal gas is taken from state 1 to state 2. How does the volume change? The P-T diagram is as shown.
I solved it in the following way:
From the diagram it is clear that P/T is a constant. From ideal gas equation,
PV = nRT
V = (nR)/(P/T)
= constant
But the answer given in my book is that volume increases. I think the book answer is wrong. What do you say Sir?
 

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  • #2
Amith2006 said:
Sir,
An ideal gas is taken from state 1 to state 2. How does the volume change? The P-T diagram is as shown.
I solved it in the following way:
From the diagram it is clear that P/T is a constant. From ideal gas equation,
PV = nRT
V = (nR)/(P/T)
= constant
But the answer given in my book is that volume increases. I think the book answer is wrong. What do you say Sir?
If the graph of P vs. T is a straight line, Volume must be constant. Is the P-T graph a straight line?

AM
 
  • #3
Amith2006 said:
Sir,
An ideal gas is taken from state 1 to state 2. How does the volume change? The P-T diagram is as shown.
I solved it in the following way:
From the diagram it is clear that P/T is a constant. From ideal gas equation,
PV = nRT
V = (nR)/(P/T)
= constant
But the answer given in my book is that volume increases. I think the book answer is wrong. What do you say Sir?
Yes Sir. It is a straight line.
 
  • #4
That would be definitely constant. Because on V=(nR)(P/T), the only value we need to consider here is P and T because it will be assume that they have the same number of n and R is constant also.
 

1. What is the Ideal Gas Equation?

The Ideal Gas Equation, also known as the Ideal Gas Law, is a mathematical relationship between the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is the pressure in Pascals, V is the volume in cubic meters, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

2. What is the significance of the Ideal Gas Equation?

The Ideal Gas Equation is used to describe the behavior of ideal gases, which are gases that follow the assumptions of the kinetic molecular theory. It is a fundamental equation in thermodynamics and is used to calculate the properties of gases, such as pressure, volume, and temperature, under different conditions.

3. How is the Ideal Gas Equation derived?

The Ideal Gas Equation is derived from the combined gas law, which states that the product of pressure and volume divided by the temperature is constant for a given amount of gas. The ideal gas constant, R, is then introduced to account for the units and to make the equation applicable to all gases.

4. What is the relationship between the Ideal Gas Equation and heat?

The Ideal Gas Equation does not directly involve heat, but it can be used to calculate the change in internal energy of an ideal gas through the equation ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the gas, and W is the work done on or by the gas. This relationship is based on the first law of thermodynamics.

5. What are the limitations of the Ideal Gas Equation?

The Ideal Gas Equation is only applicable to ideal gases, which do not exist in real life. It also assumes that the gas particles have no volume and do not interact with each other. In reality, gases do have volume and interact with each other, especially at high pressures and low temperatures. Therefore, the Ideal Gas Equation is not accurate for real gases under all conditions.

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