Question

A cycle tyre bursts suddenly. What is the type of this process?
A. Isothermal
B. Adiabatic
C. Isochoric
D. Isobaric

Answer 1

Hint: The question required knowledge of thermodynamics, more specifically the conditions governing the different kinds of mechanisms, such as isothermal (process of constant temperature), isobaric (process of constant pressure), isochoric (process of constant volume) and so on. On the basis of the conditions of such a different process, you can solve this problem.

Complete step-by-step answer:
A cycle tyre bursting suddenly, this by itself suggests that it is a spontaneous process.
Hence, the heat exchange between the body and surroundings is equal to zero.
\[\Rightarrow \Delta Q=0.\]
Let’s consider what are the conditions for different processes:
i. Isochoric process: This process occurs when the volume of the body remains constant throughout the process. \[\Rightarrow \Delta V=0.\] We know that, $dQ=dU+dW$ and $dW=PdV.$
Here,$dV=0\Rightarrow dQ=dU.$

ii. Isobaric process: This process occurs when the pressure of the body remains constant throughout the process. \[\Rightarrow \Delta P=0.\] We know that, $dQ=dU+dW$ and $dW=PdV.$
Here,$dP=0$ and $PV=nRT$ for an ideal gas. Hence, differentiating the ideal gas equation, $PdV+VdP=nRdT,$ using the isobaric condition, we get, $PdV=nRdT,\therefore dQ=dU+nRdT.$

iii. Isothermal process: This process occurs when the temperature of the body remains constant throughout the process. \[\Rightarrow \Delta T=0.\] We know that, $dQ=dU+dW$ and $dW=PdV.$
Here,$dT=0$ and $PV=nRT$ for an ideal gas. Hence, differentiating the ideal gas equation, $PdV+VdP=nRdT,$ using the isothermal condition, we get, $PdV=-VdP,\therefore dQ=dU-VdP.$

iv. Adiabatic process: This process occurs when no heat exchange occurs throughout the process. \[\Rightarrow \Delta Q=0.\] We know that, $dQ=dU+dW$ and $dW=PdV.$
Here, $dQ=0$ and upon using the adiabatic condition, we get, $0=dU+PdV,\therefore dU=PdV.$
Getting back to the problem being asked in the question, the bursting of a tyre is an instantaneous process, that is already established earlier. Hence, it follows the adiabatic process.

Note: In case you don’t remember any of the processes, remembering the process by the name is easier. Like, isothermal has thermal in it stating temperature constant process and isobaric has bar in it which refers to an unit of pressure, hence, constant pressure process.
Remember, that the tyre has an insulating rubber on itself, this keeps the air inside and outside insulated from each other, effectively making the heat exchange between the body (inside the tyre) and surrounding impossible in that instant, the tyre bursts.