Solving Isothermal Expansion of an Ideal Monatomic Gas

In summary, the conversation is about an ideal monatomic gas being expanded and then re-compressed isothermally. The questions involve finding the functions for the expansion and temperature, determining the maximum temperature and corresponding volume, calculating work done, internal energy change and heat taken in, and finding the efficiency. The individual has attempted part a by using the slope formula and part c by using the ideal gas law, but is stuck on parts b, c and e due to missing information. They believe they can do parts d, e and f if they figure out the rest.
  • #1
ilovephysics
18
0
ok i really don't understand this question, especially about finding the functions for the recompressed isothermal and about the recompression stuff, I am just stuck

An ideal monatomic gas is expanded from initial volume V1 = 1 litre, P1 = 2atm, and T1 = 300K to a volume V2 = 2 litres, and P2 = 1atm. The expansion is performed along a straight line in the PV-diagram. It is then re-compressed isothermally to its original values. a) find the function P(V) describing the expansion b) find the function T(V) during the expansion c) at which volume is the temperature a maximum Tmax and what is the volume Vm at this maximium temperature Tmax? d) what is the work done, the change in internal energy and the heat taken in during the temperature increase T to Tmax? e) what are these values for the final part of the expansion Vm to V2? f) fint the efficiency

for the parts about work done and internal energy i think i know how to do those, by using formulas like dU=nCvdT, I am just not sure

also does this question have anything to do with adiabatic processes? i don't think it does...but correct me if I am wrong, thanks!
 
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  • #2
What parts of this problem have you attempted ? Please show your work first.

No, this question has nothing to do with adiabatic processes (but that should be for you to figure out).
 
  • #3
k for part a i used p1, v1, v2, and p1, to find the slope which is rise/run and the slope is -1, i then plugged this into y=mx+b substituting p1 as y and v1 as x, and found b to be 3, so the equation i got is P(V) = -V + 3, which i don't know if its right or not..part b i have no idea how to do because i don't have T2 given so i can't find slope and do wht i did in part a, part c i tried to use pv=nrt and isolate T but I am stuck because i don't know the V at Tmax, and i don't know Tmax so i have 2 unkowns..and i think i could do parts d,e and f if i figure the rest out
 
Last edited:

1. What is an isothermal expansion of an ideal monatomic gas?

An isothermal expansion is a process in thermodynamics where an ideal monatomic gas expands at a constant temperature.

2. How is the ideal gas law used to solve isothermal expansion?

The ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are related by the equation PV = nRT, can be used to solve isothermal expansion by manipulating the variables to find the change in volume.

3. What is the equation used to calculate the work done during isothermal expansion?

The equation used to calculate the work done during isothermal expansion is W = nRT ln(V2/V1), where n is the number of moles of gas, R is the gas constant, T is the temperature in Kelvin, and V2 and V1 are the initial and final volumes, respectively.

4. How does the temperature remain constant during isothermal expansion?

The temperature remains constant during isothermal expansion because the gas is in thermal equilibrium with its surroundings, meaning that as the gas expands, it absorbs heat from its surroundings and maintains a constant temperature.

5. What are some real-life applications of solving isothermal expansion of an ideal monatomic gas?

Some real-life applications of solving isothermal expansion include refrigeration systems, air conditioning units, and the operation of internal combustion engines.

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