PhysicsBowl 2019 Q50

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PhysicsBowl 2019

50) This gas undergoes a reversible isothermal process. We need to find the work done through this process. We know that the process takes place at a temperature T[0], and the volume of the gas starts at V[0] and ends at V[1].

In an isothermal process the temperature is constant, so using the ideal gas law, we can find an equation relating pressure and volume.

Where P is pressure, V is volume, n is number of moles, R is the universal gas constant, and T[0] is the temperature

For thermodynamic processes, we can use this general formula to find the work done by the gas.

Where W is work, V is volume, and P is pressure

Now, by integrating the equation we found above, we will come up with an equation for the work done during this process.

Where P is pressure, n is number of moles, R is the universal gas constant, T[0] is the temperature, V is volume, and W is work

Finally, since the question told us that the process includes 1 mole of gas, we find that the work is nRT[0]*ln(V[1]/V[0]).

Answer: E