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 s is at a temperature of 50°c while that in 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 the reasoning behind your answers.
a) the pressure in a is higher than in b
b) there are more molecules in a than in b
c) a and b cannot 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

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

Explanation:

Given that

Size of boxes are equal

So volume of boxes = V

Temperature in box A =50°C = 323 k

Temperature in box B = 10°C = 283 K

We know that for ideal gas

P V = m R T

The mass of gases is not given so we can not say that which have high temperature.Also be can not say that which box have more molecule.

We know that average kinetic energy is directly proportional to the absolute temperature of gas that is why we can say that box A will have more kinetic energy because it have high temperature.We know that is gas have high kinetic energy then we can say that it have high moving velocity.

So the option d and e is correct.

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

Here we have a problem with ideal gases.

The solutions are:

Remember that the ideal gas equation is:

where:

Here we have two equal size boxes A and B, so we have:

We also know that:

With this information, we want to see which options can be true.

a) "The pressure in A is higher than in B"

Notice that pressure depends linearly with the temperature, box A has a larger temperature than box B, then probably box A will also have a larger pressure than box B, but this only would be true if the number of mols is the same in both boxes ( or really similar).

So this can be true.

b) "There are more molecules in A than in B"

Similar to before, for given values of pressures, this can be true, but is not always true.

c) "The molecules in A have more average kinetic energy per molecule than those in B"

Temperature manifests as an increase in kinetic energy of the molecules, thus, box A has a larger temperature than box B, then this is true.

d) "The molecules in A are moving faster than those in B"

We know that the molecules in the box A have larger kinetic energy than the ones in the box B, but that does not imply that the molecules have a larger velocity, because the masses can be different.

So this can be true, it depends on the masses of the molecules in each box.

If you want to learn more, you can read:

link