Isothermal Expansion, No Calculus

V1=444, V2=V1e(P2/P1), P1=2.52e5, P2=0.857e5In summary, the gas in the container at high pressure is allowed to expand at constant temperature until it reaches atmospheric pressure. The work done on the gas can be calculated using the formula W=PVln(V2/V1) where V1 is the initial volume, V2 is the final volume, P1 is the initial pressure, and P2 is the final pressure. The change of internal energy is zero and the amount of heat done on the gas is equal to the work done.
  • #1
Alexandra_H
1
0

Homework Statement



"We have some gas in a container at high pressure. The volume of the container is 444 cm^3. The pressure of the gas is 2.52e5 Pa. We allow the gas to expand at constant temperature until its pressure equals atmospheric pressure, which is 0.857e5 Pa."

A. Find the work (J) done on the gas.
B. Find the change of internal energy (J) of the gas.
C. Find the amount of heat (J) done on the gas.

Homework Equations



First law of thermodynamics. Ideal gas laws.

The Attempt at a Solution



(A) is what I'm having trouble with. The class is not calculus-based. (B) is zero, and for (C), W = Q (appropriate signs, - and -, as they seem to be referencing the surroundings, not the gas itself)--easy enough, once I have A.

Thoughts?
Thanks!
 
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  • #2
Since you can't use calculus to derive the formula, I think you'd just need to use the direct result:

W=PVln(V2/V1)
 

1. What is isothermal expansion?

Isothermal expansion refers to a process in thermodynamics where a gas expands at a constant temperature. This means that the internal energy of the gas remains constant during the expansion.

2. What is the formula for calculating isothermal expansion?

The formula for calculating isothermal expansion is given by the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

3. How is isothermal expansion different from adiabatic expansion?

Isothermal expansion occurs at a constant temperature, while adiabatic expansion occurs without any heat exchange with the surroundings. This means that in isothermal expansion, the temperature remains constant, while in adiabatic expansion, the temperature changes.

4. What are some real-life examples of isothermal expansion?

Some real-life examples of isothermal expansion include aerosol cans, where the gas inside expands at a constant temperature to push out the contents, and refrigerators, where the expansion of gas inside the cooling system helps to lower the temperature.

5. Why is isothermal expansion important in thermodynamics?

Isothermal expansion is important in thermodynamics because it helps us understand the behavior of gases under certain conditions. It also has practical applications in various industries, such as refrigeration and air conditioning.

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