Gas pressure within a fixed container will increase when 1) gas is cooled 2) gas is heated 4) gas volume changes 5) mass of a gas is increased

2) gas is heated

Explanation:

In this problem, we have a gas in a fixed container (so, the volume of the gas does not change). Let's see what happens in the different situations listed in the question.

1) Gas is cooled. Since the volume if fixed, the work done by the gas is zero: This means that the change in internal energy of the gas is equal to the heat exchanged: . However, since the gas is cooled, this means that Q is negative (heat is removed from the gas), so is negative, so the temperature of the gas, T, is decreased. Now if we look at the ideal gas equation

We see that since V, n and R remain constant, a decrease in T corresponds to a decrease in p: so, the pressure of the gas decreases.

2) Gas is heated. If we apply exactly the same reasoning of point 1), we see that when the gas is heated, its temperature increases: therefore, according to the ideal gas equation, its pressure must increase as well.

3) Gas volume change. By looking again at the ideal gas equation:

We see that in this case we don't have enough information to determine how does the gas pressure change. In fact, we don't know whether the volume V increases or decreases, so we cannot determine how p changes.

5) mass of a gas is increased. An increase in the mass of the gas corresponds to an increase in the number of moles, n. However, in the ideal gas equation, we don't know if the temperature of the gas, T, remains the same or not: therefore, we don't have enough information to tell how does p change.

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