How Does Isothermal Expansion Affect Work Done and Temperature in an Ideal Gas?

In summary, the conversation discusses an isothermal expansion of a monatomic ideal gas and asks for the temperature at the beginning and end of the process, as well as the work done by the gas. The formula pV=nRT is used to solve for temperature, and the work done is calculated using the formula W=nRTln(V_f/V_i). The temperature is found to be constant and the work done is 1670.42 joules.
Suppose 145 moles of a monatomic ideal gas undergo an isothermal expansion from 1.00m^3 to 4.00m^3, as shown in figure. what is the temp at the beginning and end of this process? how much work is done by the gas during the expansion?

http://www.physics.brocku.ca/Courses/1p23/images/FG18_24.JPG

since it is isothermal the temperature is constant correct?
so to solve for the temperature would i just use pv=nrt with the respective values for pressure and volume?
and for the work done W=nrtln(vf/vi)

thanks

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You have p_i and p_f, and also v_i and v_f. Can you think of a formula that uses p and v ?

Hint: What are the units for pressure?

so i wouldn't use pv=nrt?

Try it out. Plug in the values of p_i and v_i into that formula.
Then plug in the values of p_f and v_f into that formula.
See what you get.

im getting .332 for the temperature.

and for the work i get 1670.42j

Now you tell me. Is temperature constant?

yup yup. thought it was tryin to trick me by askin the temp of beginnin and end like it was going to be two different values.

1. What is isothermal expansion?

Isothermal expansion is a thermodynamic process in which a gas expands at a constant temperature. This means that the internal energy of the gas remains constant while the volume and pressure change.

2. How is isothermal expansion different from adiabatic expansion?

In isothermal expansion, the temperature remains constant, while in adiabatic expansion, there is no heat exchange with the surroundings. This means that in isothermal expansion, the gas is in thermal equilibrium with its surroundings, while in adiabatic expansion, the gas is not in thermal equilibrium.

3. What is the formula for calculating the work done in an isothermal expansion?

The formula for calculating work done in an 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, V2 is the final volume, and V1 is the initial volume.

4. How does an isothermal expansion affect the pressure and volume of a gas?

In an isothermal expansion, as the gas expands, its volume increases and its pressure decreases. This is because the temperature remains constant, so the gas molecules have the same average kinetic energy, but are spread out over a larger volume, resulting in a decrease in pressure.

5. Can you give an example of an isothermal expansion in real life?

One example of an isothermal expansion in real life is the expansion of a balloon as it is filled with air. The temperature of the air inside the balloon remains constant, while the volume of the balloon increases. This is because the air inside the balloon is in thermal equilibrium with the surrounding air, so the temperature remains constant during the expansion process.

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