Thermodynamic Cycle: Calculating Heat Transfer and Work

[kdinser]

Sorry about the double post, I had technical difficulties that I was working on and the title of my orginal post got screwed up.

I'm having problems getting started on this one.

A gas undergoes a thermodynamic cycle consisting of 3 processes

process 1-2 compression with pressure(p)*volume(V) = constant, from
$$p_{1} = 1 bar$$
$$V_{1} = 1.6m^3$$
to
$$p_{2} = ?$$
$$V_{1} = .2m^3$$

$$U_{2}-U_{1}=0$$

process 2-3
Constant pressure to $$V_{3}=V_{1}$$

process 3-1
Constant Volume, $$U_{1}-U_{3} = -3549kJ$$

There are no significant changes in kinetic or potential energy.
Determine the heat transfer and work for process 2-3 in kJ.

I don't have any problems finding$$p_{2}$$ or the work needed to compress the gas, but I'm not really sure where to go from there.

$$p_2=\frac{p_1V_1}{V_2}$$

$$W=\int p dV$$

When I work these out, I end up with 333kJ for W and 8 bar for p2.

If someone could give me a quick push in the right direction, that would be great.

 

[Andrew Mason]

A gas undergoes a thermodynamic cycle consisting of 3 processes

process 1-2 compression with pressure(p)*volume(V) = constant, from
$$p_{1} = 1 bar$$
$$V_{1} = 1.6m^3$$
to
$$p_{2} = ?$$
$$V_{1} = .2m^3$$

$$U_{2}-U_{1}=0$$

process 2-3
Constant pressure to $$V_{3}=V_{1}$$

process 3-1
Constant Volume, $$U_{1}-U_{3} = -3549kJ$$

There are no significant changes in kinetic or potential energy.
Determine the heat transfer and work for process 2-3 in kJ.
.

The work done between 2-3 is just $P_2\Delta V = P_2(V_3-V_2) = P_2(7*V_2)$

The change in internal energy is $U_3-U_2 = U_3-U_1$, since $U_2=U_1$

Use $\Delta Q = \Delta U + W$ to find the energy (heat) flow into the system.

AM

 

[quicknote]

As a scientist, your first step in solving this problem would be to identify the type of thermodynamic cycle that is occurring. In this case, it appears to be a closed system cycle, where the gas is compressed and then expanded back to its original volume. This is known as a Brayton cycle.

Next, you would use the known values for pressure and volume in process 1-2 to calculate the specific gas constant, R, using the ideal gas law (pV=nRT). Then, using the given information for process 3-1, you can calculate the change in internal energy (ΔU) for the entire cycle.

Once you have the change in internal energy, you can use the First Law of Thermodynamics (ΔU = Q - W) to calculate the heat transfer (Q) for process 2-3. Since there are no significant changes in kinetic or potential energy, the change in internal energy is equal to the heat transfer for this process.

Finally, you can use the work equation you have already calculated (W = ∫p dV) to solve for the work done in process 2-3. This will give you the final answer for the heat transfer and work in process 2-3 in kJ.