P.3.6.2.2 Ideal Gases

The graph shows the variation of pressure p with temperature θ for a fixed mass of an ideal gas at constant volume.

What is the gradient of the graph?

• 0.341

• 0.395

• 2.93

• 5.00

Two flasks X and Y are filled with an ideal gas and are connected by a tube of negligible volume compared to that of the flasks. The volume of X is twice the volume of Y.X is held at a temperature of 150 K and Y is held at a temperature of 300 K.

What is the ratio shown?

• 0.125

• 0.25

• 4

• 8

What is the total internal energy of 2.4 mol of an ideal gas which has a temperature of 15 °C?

• 6.0 × 10^–21 J

• 1.4 × 10^–20 J

• 4.5 × 10² J

• 8.6 × 10³ J

Specimens P and Q of the same gas exert the same pressure. P is at a temperature of 280 K and contains 10²⁰ molecules per unit volume. The temperature of Q is 350 K.

What is the number of molecules per unit volume in Q?

• 0.09 × 10²⁰

• 0.75 × 10²⁰

• 0.80 × 10²⁰

• 1.25 × 10²⁰

One mole of gas occupies a volume V at a pressure p and Celsius temperature θ.

The graphs, A to D, show variation of pV with θ.

Line X is for one mole of nitrogen and line Y is for one mole of oxygen.

Relative molecular mass of nitrogen = 28

Relative molecular mass of oxygen = 32

Which graph is correct?

• A

• B

• C

• D

X and Y are two gas bottles that are connected by a tube that has negligible volume compared with the volume of each bottle.

Initially the valve W is closed.

X has a volume 2V and contains hydrogen at a pressure of p.

Y has a volume V and contains hydrogen at a pressure of 2p.

X and Y are both initially at the same temperature.

W is now opened. Assuming that there is no change in temperature, what is the new gas pressure?

• 
• 
• 
• 

Which one of the graphs below shows the relationship between the internal energy of an ideal gas (y-axis) and the absolute temperature of the gas (x-axis)?

• A

• B

• C

• D

The diagram shows the p-V diagram of an ideal hot-air engine. WX and YZ are isothermal changes.

Which line of the table below correctly indicates the nature of the work done on or by the air in each part of the cycle?

• A

• B

• C

• D

The temperature of a room increases from 283K to 293K. The r.m.s. speed of the air molecules in the room increases by a factor of

• 1.02

• 1.04

• 1.41

• 2.00

A fixed mass of an ideal gas initially has a volume V and an absolute temperature T. Its initial pressure could be doubled by changing its volume and temperature to

• V/2 and 4T

• V/4 and T/2

• 2V and T/4

• 4V and 2T