Chapter U3, Problem 11STP

Interpretation Introduction

Interpretation:

The behavior of gas particles inside a gas balloon needs to be explained which travels to a high altitude.

Concept introduction:

The pressure (P), volume (V) and the absolute temperature (T) of an ideal gas is related by the ideal gas law as follows:

$\text{PV = nRT}$

Where n is the number of moles of the ideal gas taken and R is the Universal gas constant.

It can be seen from the above relationship that

$\text{V =}\frac{\text{nRT}}{\text{P}}$

Thus, a lowering of the pressure of the gas leads to an increase in volume and vice versa. Temperature has a more direct influence on the volume of the gas; a lowering of temperature reduces the volume of the gas and vice versa.

Answer to Problem 11STP

Option (A) is the correct answer.

Explanation of Solution

Reason for Correct Option:

The pressure of a fixed mass of gas falls with increasing altitude. Thus, the gas will have lower atmospheric pressure at a high altitude than at the ground level.

As per the kinetic molecular theory of gases, the pressure of a gas is directly proportional to the number of collisions of the gas molecules with the walls of the container and between themselves. Thus, a low pressure will indicate fewer collisions between the gas particles and consequently, the particles will have more space to move around, thereby, leading to an expansion in volume of the gas.

Conclusion

Reasons for Incorrect Options:

The second option, option (B) is incorrect because the pressure of the gas decreases with increasing altitude.

It has been stated that the pressure of a gas arises due to molecular collisions and a lower pressure is simply indicative that there are fewer collisions between the gas particles; thus, the third option, option (C) is incorrect.

Further, the temperature of an ideal gas decreases with increasing altitude. As per the kinetic molecular theory of gases, the average speed of gas particles depends only on the absolute temperature of the gas. A lower temperature of the gas indicates that the gas particles have lower average speeds, thereby, resulting in fewer collisions. Thus, the last option, option (D) is incorrect.