Question

We have two equal-size boxes, A and B. Each box contains gas that behaves as an ideal gas. We insert a thermometer into each box and find that the gas in box A is at 50°C while the gas in box B is at 10°C. This is all we know about the gas in the boxes. Which of the following statements must be true? Which could be true? Explain your reasoning. (a) The pressure in A is higher than in B. (b) There are more molecules in A than in B. (c) A and B do not contain the same type of gas. (d) The molecules in A have more average kinetic energy per molecule than those in B. (e) The molecules in A are moving faster than those in B.

Short answer

1. Statement is true
2. Statement is false
3. Statement is false
4. Statement is true
5. Statement is false

Step-by-step solution

Step 1:

Given data:

The temperature of the gas inside box A is

The temperature of the gas inside box B is

1. Ideal gas equation is

As the two boxes have the same volume as they are of the same size of boxes. And astherefore, the gas having lower volume will have higher pressure.

And as the higher-pressure gas has a higher temperature. Therefore, the temperature of box A is higher than the temperature of a gas in box B. So, the pressure in box A is higher than the pressure in box B.

Hence, the statement is true.

Step 2:

a. Ideal gas equation is

As the pressure isn’t given, taking three cases

As for the temperature ,so if the pressure is equal, no. of molecules at box B is greater than in box A.

And if the pressure isn’t equal, no. of molecules in both boxes depend on the value of pressure compared with the temperature in the same boxes.

Hence, the statement is false.

Step 3:

b. Ideal gas equation is

And as pressure isn’t given, therefore taking three cases

And as,

but the mass of gas doesn’t depend on pressure or volume of temperature, it depends on the structure of the gas.

Hence, the statement is false.

Average kinetic energy per molecule depends only on temperature.

And as then for molecule in A have more K.E than those of B.

Hence, the statement is true.

Step 4:

(d). Ideal gas equation is

The root-mean-square speed of the gas molecule is given by

And as ,the mass of gas doesn’t depend on pressure or volume, it depends on its internal structure. Therefore, it is not possible whether the two gases have the same masses or different masses.

Hence, the statement is false.