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

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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

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A guide to all 4 processes:

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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.