Question

Two moles of an ideal gas, in an initial state P = 10 atm, V = 5 liters, are taken, reversibly, in a clockwise direction, around a circular path given by (V -10)2 + (p-10)2=25. Calculate the amount of work done by the gas as a result of this process, and calculate the maximum and minimum temperatures attained by the gas during the cycle.

Answer 1

To calculate the work done by the gas, find the area enclosed by the circular path in the pressure-volume diagram. To calculate the maximum and minimum temperatures attained by the gas during the cycle, use the ideal gas law.

Step-by-step explanation:

In order to calculate the work done by the gas, we need to calculate the area enclosed by the circular path in the pressure-volume (PV) diagram. The equation of the circular path is given by (V - 10)2 + (P - 10)2 = 25. We can rewrite this equation as V2 - 20V + P2 - 20P + 25 = 0.

Using this equation, we can find the values of V and P at the intersection points of the circular path.

To calculate the maximum and minimum temperatures attained by the gas during the cycle, we need to use the ideal gas law. The relationship between pressure, volume, and temperature for an ideal gas is given by PV = nRT, where n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. We can rearrange this equation to calculate the temperatures at the initial and final states of the cycle.