An ideal gas, at initial temperature T1 and initial volume 3.1 m3, is expanded adiabatically to a volume of 7.1 m3, then expanded isothermally to a volume of 23 m3, and then compressed adiabatically back to T1. What is its final volume?

10.0 m³

Explanation:

The gas initially starts expanding adiabatically from state 1 until it reaches state 2, with V2 being 7.1 m³ then it goes on to continue on to state 3 isothermally, with V3 being 23 m³ and finally gets compressed adiabatically to reach state 4.

For the adiabatic process in stage 1 to 2, we have that

P1V'1 = P2V'2

For the isothermal process in stage 2 to 3, we have that

P2V2 = P3V3

For the adiabatic process in stage 3 to 4, we have that

P3V'3 = P4V'4

Starting from the ending, we see that

P4 = P3 * (V3/V4)',

Going backwards we see that

P4 = P2 * (V2/V3) * (V3/V4)'

Going further backwards, we see that

P4 = P1 * (V1/V2)' * (V2/V3) * (V3/V4)'

We substitute expression for P4 into the equation P1V1 = P4V4 with T being constant, and then get V1V3 = V2V4

Trying to solve for V4, we get

V4 = V1V3/V2

V4 = (3.1 * 23) / 7.1

V4 = 71.3 / 7.1

V4 = 10.0 m³

what are the options.

explanation:

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.