Question

mary wants to remove a dent from a ping - pong ball without cutting into the sealed ball. she decides to put the ball in a bowl of boiling water. after a while, mary observes the dent disappearing until it is no longer present. why did the dent disappear?
the water caused an increase in temperature of the air inside the ball and a decrease in pressure.
the water caused an increase in temperature of the air inside the ball and an increase in pressure.
the water caused a decrease in temperature of the air inside the ball and a decrease in pressure.
the water caused a decrease in temperature of the air inside the ball and an increase in pressure.

Explanation:

To solve this, we analyze the gas laws (specifically Charles's law or ideal gas law concepts). When the Ping - Pong ball is placed in boiling water, the air inside the ball absorbs heat from the hot water. According to the ideal gas law ($PV = nRT$), when the volume ($V$) of the gas (air inside the ball, assuming the ball's material is somewhat flexible but the initial volume change due to dent is considered, and $n$ (moles of gas) is constant as the ball is sealed), an increase in temperature ($T$) will lead to an increase in pressure ($P$) if the volume is constrained or will cause the gas to expand. The boiling water is at a high temperature, so the air inside the ball gets heated (temperature increases). As the temperature of the air inside the ball increases, the air molecules move faster and collide more frequently with the inner surface of the ball. This increased collision rate leads to an increase in pressure inside the ball. The increased pressure inside the ball then pushes against the dent, causing it to pop out.

Now let's analyze each option:

• Option 1: Says temperature increases and pressure decreases. But according to gas laws, with constant volume (or when the gas can expand against the dent), an increase in temperature should lead to an increase in pressure (or expansion which can be related to pressure increase). So this is incorrect.
• Option 2: States that the water (boiling, so high temperature) causes an increase in temperature of the air inside the ball and an increase in pressure. This matches our analysis.
• Option 3: Claims temperature and pressure decrease. But the ball is in boiling water, so temperature should increase, not decrease. So this is wrong.
• Option 4: Says temperature decreases and pressure increases. But the ball is in boiling water, so temperature should increase, not decrease. So this is incorrect.

Answer:

B. The water caused an increase in temperature of the air inside the ball and an increase in pressure.