# Relationship between pressure and volume

1. May 12, 2006

### Amith2006

Sir,
Two different isothermal curves representing the relationship between pressure and volume at a given temperature of the same ideal gas are shown for masses M1 and M2 of the gas respectively in the following figure, then which is greater M1 or M2?

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• ###### Diagram3.bmp
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2. May 12, 2006

### Curious3141

b) I can't see the attachment, but here's a hint : what does the Ideal Gas Law state? How does this bear on your problem?

3. May 14, 2006

### Amith2006

Sir,
I solved it the following way:
From the figure T1>T2. But according to ideal gas law, Temperature is inversely proportional to mass of gas. Therefore M1<M2.Is it right?

4. May 14, 2006

But the question states that the ideal gas is at a given temperature. Doesn't this mean that T1=T2?

5. May 14, 2006

### maverick280857

The ideal gas equation says
$$PV = nRT$$
The number of moles of the gas is given by (m = mass of gas, M = molar mass)
$$n = \frac{m}{M}$$
So
$$PV = \frac{m}{M}RT$$
Solving for m, the mass of the gas
$$m = \frac{PV}{RT}M$$

If you draw a vertical line (parallel to the P-axis) it cuts the two curves at pressures $P_{2}$ and $P_{1}$. Clearly $P_{2} > P_{1}$. Also $T_{2} > T_{1}$ (can you see why???). I think I have said more than enough.

Amit, it is not correct to say that the temperature is inversely or directly proportional to the mass of the gas unless pressure and volume are constant. As you can see here, pressure and temperature are different for the two gases.

6. May 14, 2006

### maverick280857

Do you know what an isotherm is?

7. May 14, 2006

### Andrew Mason

I would agree with Pizzasky's interpretation of the problem. The two graphs are the isotherms for two different quantities of the same gas for the same temperature. Since PV (the area of the rectangle with corners on the origin and on the curve) is greater for M2, this means that n2RT > n1RT so M2>M1.

AM

8. May 14, 2006

### maverick280857

If you say that the temperatures are equal, then you and Pizzasky are correct. It seems that the wording suggests so. Fine.

9. May 14, 2006

### Gokul43201

Staff Emeritus
Maverick,

I agree with AM and Pizza. If the number of moles of the gas is unknown, you can't say that the outer isotherm corresponds to a higher temperature. An isotherm that is farther from the origin can also be generated at the same temperature by increasing the number of moles in the sample.

In this case, if you allow the number of moles (through the total mass) and the temperature to float, you can't make any meaningful comparison. One of the two must be fixed, and that would be the temperature.

Edit : I wrote this before I saw your last post.