Isobaric Expansion: Finding Internal Energy & Heat w/ 2.0 Moles Ideal Gas

[jesuslovesu]

I have a Pressure vs Volume Graph and A -> B.
It's just an isobaric expansion, the work done by the gas is -3600 J.
The gas is monatomic ideal (2.0moles).
If I used it correctly, PV=nRT, I found the change in temperature to be 216.6K.

My question is: How do I find the change in internal energy and heat? I don't have any info about the gas except that it's ideal and 2.0 moles worth.

 

[Chi Meson]

Use the equation for the amount of heat required to change the temperature of that gas (at constant pressure). You will have W and Q, then find delta U using the First Law.

 

[kyle8921]

To find the change in internal energy and heat in an isobaric expansion, we can use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system. In this case, we know that the work done by the gas is -3600 J, so we can calculate the change in internal energy using the equation ΔU = Q - W.

To find the heat, we can use the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Since this is an isobaric expansion, the pressure remains constant at all points on the graph. Therefore, we can rearrange the ideal gas law to solve for the temperature at point A and point B, using the given values of pressure, volume, and number of moles.

At point A, we have P = 1 atm, V = V_A, n = 2.0 moles, and we can solve for T_A. Similarly, at point B, we have P = 1 atm, V = V_B, n = 2.0 moles, and we can solve for T_B. The change in temperature (ΔT) can then be calculated by subtracting T_A from T_B.

Now that we have the change in temperature, we can use the specific heat capacity (c) of a monatomic ideal gas to calculate the heat (Q) added to the system. The specific heat capacity of a monatomic ideal gas is given by c = (3/2)R, where R is the gas constant. Therefore, we can calculate the heat using the equation Q = n*c*ΔT.

Finally, we can plug in the values for Q and W into the first law of thermodynamics equation to find the change in internal energy (ΔU). Keep in mind that the work done by the gas is negative (-3600 J), so we will need to add it to the heat (Q) in order to calculate the change in internal energy.

In summary, to find the change in internal energy and heat in an isobaric expansion, we can use the first law of thermodynamics and the ideal gas law, along with the specific heat capacity for