Question

Consider a gas where the initial state is 1 mol, P? = 4 atm, V? = 2L and U? = 560 J and the final state is 1 mol, P? = 3 atm, V? = 4 L and U? = 990 J. The process is quasi-static and 1 L atm = 101.325 J. a) The gas is allowed to expand at constant pressure to a volume of 4 L. If is then cooled at constant volume until its process is 3 atm. Show this process on a PV diagram and calculate the work done by the gas and the heat added during the process. b) The gas is first cooled at constant volume until its pressure is 3 atm. It is then allowed to expand at constant pressure until its volume is 4 L. Show this process of a PV diagram and calculate the work done by the gas and heat added to the process.

          Consider a gas where the initial state is 1 mol, P? = 4 atm, V? = 2L and U? = 560 J and the final state is 1 mol, P? = 3 atm, V? = 4 L and U? = 990 J. The process is quasi-static and 1 L atm = 101.325 J.
a) The gas is allowed to expand at constant pressure to a volume of 4 L. If is then cooled at constant volume until its process is 3 atm. Show this process on a PV diagram and calculate the work done by the gas and the heat added during the process.
b) The gas is first cooled at constant volume until its pressure is 3 atm. It is then allowed to expand at constant pressure until its volume is 4 L. Show this process of a PV diagram and calculate the work done by the gas and heat added to the process.

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Consider a gas where the initial state is 1 mol, P? = 4 atm, V? = 2L and U? = 560 J and the final state is 1 mol, P? = 3 atm, V? = 4 L and U? = 990 J. The process is quasi-static and 1 L atm = 101.325 J.
a) The gas is allowed to expand at constant pressure to a volume of 4 L. If is then cooled at constant volume until its process is 3 atm. Show this process on a PV diagram and calculate the work done by the gas and the heat added during the process.
b) The gas is first cooled at constant volume until its pressure is 3 atm. It is then allowed to expand at constant pressure until its volume is 4 L. Show this process of a PV diagram and calculate the work done by the gas and heat added to the process.

Added by Tammy A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

08/08/2023

Step 1

The final state is given as P2 = 3 atm, V2 = 4 L, and U2 = 990 J. The process is quasi-static and at constant temperature T = 101.325 J. We can use the first law of thermodynamics to calculate the heat added to the system during the process: ΔU = Q - W where ΔU Show more…

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Transcript

00:01 Hello students, here the condition for quasi -static process is given.

00:06 First we need to draw p -v diagram that is pressure along y -axis, volume along x -axis.

00:19 In the question given that initially the gas is at 4 atmospheric pressure and at this condition volume v1 is 2 liter.

00:34 Then the gas is expanded and it comes to 3 atmospheric pressure.

00:46 At that time the volume is v2 which is 4 liter.

00:54 So this shows p -v diagram for the given process.

00:59 Now we need to calculate work done.

01:04 Work done is given by area under the curve.

01:09 So we know that work done is nothing but pressure into volume.

01:13 For pressure we can consider 4 atmospheric pressure.

01:18 At that time volume is 2 liter.

01:25 Now for atmospheric pressure substitute 1 .013 into 10 power 5 which is in pascal.

01:35 Given that atmospheric pressure is 101 .325 joules but we are converting it to pascal by first converting to kilo joule that is 101325 and then kilo is kept at 10 power 5.

01:55 Now 2 liter is converted to meter cube which is nothing but 2 into 10 power minus 3.

02:01 From this calculation we obtain work done is equal to 904 joules.

02:09 Here we can observe work is done at this portion.

02:21 Next we need to calculate change in internal energy which is given by u2 minus u1.

02:32 Substitute for u2 990 joules minus u1 560 joules.

02:38 From this we get 430 joules...

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