Please check my answers. Identify the following processes as isothermal, isovolumetric, or adiabatic:

a. a tire being rapidly inflated- adiabatic
b. a tire expanding gradually while heating- isothermal
c. a tire being heated while in a rigid metal container- isovolumetric

c.isovoluetric

1) Adiatic since the system is rapidly inflated as there was no time for the transfer of energy as heat

2) Isothermal as the system is being heated at a constant temperature, doesnt changes the internal energy of the system

3) Isovolmetric because the tire is being heated while in a rigid metal container so metal container wouldnt expand any more due to which the tire is being heated no work is done on or by the system since the volume is constant

c. The process of a tire being heated while in a rigid metal container is called isochoric or isovolumetric. This means that the volume of the system remains constant during the heating process.

To identify the processes as isothermal, isovolumetric, or adiabatic, you need to understand the characteristics of each process:

1. Isothermal process: In an isothermal process, the temperature remains constant. This means that there is no change in the internal energy of the system. This process usually occurs when heat is continuously transferred in or out of the system to maintain a constant temperature.

2. Isovolumetric (isochoric) process: In an isovolumetric process, the volume remains constant. This means that there is no work done by or on the system due to volume change. The process typically occurs in a system with fixed boundaries, such as a container, where the volume cannot change.

3. Adiabatic process: In an adiabatic process, there is no heat exchange between the system and its surroundings. This means that no heat is added to or removed from the system. The process is typically characterized by the work done on or by the system to change its internal energy.

Now let's analyze the given processes:

a. A tire being rapidly inflated: In this case, rapid inflation of the tire implies a quick change in volume. Since there is no mention of temperature change or heat transfer, we can infer that the process is adiabatic.

b. A tire expanding gradually while heating: The expansion of the tire indicates a change in volume. Additionally, the mention of heating implies the addition of heat, suggesting that the process is not adiabatic. Since there is no mention of a constant temperature, we cannot conclude it is isothermal. Therefore, we can deduce that the process is not isothermal or adiabatic, leaving isovolumetric as the most likely option.

c. A tire being heated while in a rigid metal container: The fact that the tire is in a rigid metal container implies that the volume remains constant. Moreover, there is mention of heating, indicating that heat is added to the system. Since there is no mention of a temperature change, we can conclude that the process is isovolumetric.

So, based on the given descriptions, the correct identification of the processes is as follows:

a. a tire being rapidly inflated - adiabatic
b. a tire expanding gradually while heating - not isothermal or adiabatic (likely isovolumetric)
c. a tire being heated while in a rigid metal container - isovolumetric