Calculating Work Done by an Ideal Gas in an Isothermal Expansion

In summary, we need to use the formula w=nRTln(vi/vf) to find the work done by the gas. We can use the units of 8.314 J/mol K for R and the units for pressure and volume to yield the temperature in Kelvins. Additionally, P*V gives us a unit equivalent to joules and in a monatomic ideal gas, the internal energy is (3/2)PV.
  • #1
Rasine
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55 moles of an ideal gas, at an initial pressure of 3.00 × 105 N/m2 and an initial volume of 1.700 m3, undergo a small isothermal expansion to a volume of 1.720 m3. Find the work done by the gas.


i am confused about the units but here is what i got...

so w=nRTln(vi/vf)


so i know n and i know vi and vf...now for R i think i am going to use 8.314 J/mol K...are those the right units?


so to find T i must use PiVi=nRT

but what units does P and V have to be into yeild K and shoud use the same units for R as i wrote above?
 
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  • #2
You are using the correct formula and the correct reasoning. The constant R (8.314 N*m/mol*K) is designed specifically to give you the right units. You will get the temperature in Kelvins.

P*V, by the way, gives you a unit equivalent to joules. Pressure can be considered to be a measurement of energy per volume ratio. In a monatomic ideal gas, the internal energy of the gas is equal to (3/2)PV.
 
  • #3
thank you so much
 

1. What is the definition of work done by a gas?

The work done by a gas is the measure of the energy transferred to or from the system as a result of a change in volume and pressure.

2. How is the work done by a gas calculated?

The work done by a gas can be calculated using the formula W = PΔV, where P is the pressure and ΔV is the change in volume.

3. What is the unit of measurement for work done by a gas?

The unit of measurement for work done by a gas is joules (J), which is equivalent to Newton-meters (Nm).

4. What factors affect the work done by a gas?

The work done by a gas is affected by the initial and final volumes of the gas, as well as the pressure and the type of process (isobaric, isochoric, or adiabatic).

5. How does the work done by a gas relate to the first law of thermodynamics?

The work done by a gas is closely related to the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. The work done by the gas is a form of energy transfer, and is often a key factor in the study of thermodynamics.

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