IMAT 2017 Q59 [Ideal Gas Change]

A fixed mass of an ideal gas undergoes a change in which it is supplied with 3500 J of thermal energy. At the same time this gas does 3500 J of work on its surroundings.

Which type of change does the gas undergo during this time?

A. adiabatic
B. isothermal
C. isochoric
D. isomeric
E. isobaric


The basic processes with ideal gas are known as follows: isothermal, isochoric, isobaric, and adiabatic.

In these systems, one or more variables is held constant.

  1. Isobaric; where the pressure of the system is kept constant. \delta P=0

  1. Isochoric; where the volume of the system is kept constant. \delta V=0

  1. Isothermal; where the temperature of the system is kept constant. \delta U=0 and \delta T=0

Note that when \delta T=0, the relation between Volume and Pressure is inversely proportional.

  1. Adiabatic; where no heat is being added or removed from the system (no heat transfer). Q= 0


A guide to all 4 processes:


Our answer is B.

Note: Do not confuse the adiabatic with the isothermal, we have supplied heat to the system and work was done- therefore it cannot be an adiabatic system.

Based on the information provided, it appears that the gas undergoes an isothermal change during the time in question. An isothermal change is a type of thermodynamic process in which a system undergoes a change in temperature, but the temperature remains constant. In this case, the gas is supplied with 3500 J of thermal energy, which means that it gains heat. At the same time, the gas does 3500 J of work on its surroundings, which means that it expends energy. Since the net change in the gas’s energy is zero (3500 J gained - 3500 J expended = 0), the temperature of the gas must remain constant throughout the process. Therefore, the correct answer to the question is option B, isothermal.