Question

1. a gas in a rigid container is heated. which process best describes what happens? mark only one oval. isothermal process because heat is added adiabatic process because container is sealed isochoric process because volume is constant isobaric process because container doesnt change 26. when analyzing the force exerted by gas pressure on a container wall, which factor is most important? mark only one oval. the total kinetic energy of all gas molecules the potential energy stored in molecular bonds the specific heat of the gas the average kinetic energy per molecule and collision frequency 27. a hot air balloon rises because: * mark only one oval. hot air has lower density than cold air at the same pressure both a and c are correct hot air has higher pressure than cold air hot air has greater specific volume and lower density

Explanation:

• Question 25:
• An isothermal process requires temperature to be constant, but heating the gas will change its temperature, so the first option is wrong.
• An adiabatic process has no heat transfer, but the problem states heat is added, so the second option is wrong.
• An isochoric process has constant volume. A rigid container means volume \(V\) is constant. Using the ideal - gas law \(PV = nRT\), when \(V\) is constant (\(dV=0\)), \(P\propto T\). So this is an isochoric process.
• An isobaric process requires pressure to be constant. There is no information to suggest pressure is constant here, so the fourth option is wrong.
• Question 26:
• The force exerted by gas pressure on a container wall is related to the momentum transfer during molecular collisions. The average kinetic energy per molecule (\(\overline{K}=\frac{3}{2}kT\)) determines the speed of molecules (since \(K = \frac{1}{2}mv^{2}\)), and the collision frequency (number of collisions per unit area per unit time) also affects the force.
• The total kinetic energy of all gas molecules (\(K_{total}=n\times\frac{3}{2}RT\)) does not directly account for the force - pressure relationship in terms of molecular - wall interactions as precisely as the average kinetic energy per molecule and collision frequency.
• Potential energy in molecular bonds is not relevant to gas - pressure - induced force on the container wall.
• Specific heat (\(C\)) is related to heat capacity (\(Q = nC\Delta T\)) and not directly to the force due to gas pressure on the wall.
• Question 27:
• From the ideal - gas law \(PV=nRT\), we can express density \(

ho=\frac{m}{V}=\frac{Pm}{nRT}\) (where \(m\) is the mass of the gas and \(n\) is the number of moles). At the same pressure \(P\), for hot air (\(T\) is larger), \(
ho\) is smaller.

• Specific volume \(v=\frac{V}{m}\), and \(

ho=\frac{1}{v}\). So hot air has a greater specific volume (since \(
ho\) is smaller).

• Hot air does not have a higher pressure than cold air in the context of a hot - air balloon rising (assuming the balloon is open to the atmosphere, the pressure inside and outside (atmospheric pressure) is approximately the same at the same altitude during the rising process).

Answer:

1. Isochoric process because volume is constant.
2. The average kinetic energy per molecule and collision frequency.
3. Both A and C are correct.