Some serious help needed in thermodynamics

[rock.freak667]

Homework Statement

An insulated piston-cylinder assembly contains air and nitrogen separated by a highly conducting partition. Accordingly, the temperatures of the two gases may be assumed to be equal at all times. Initial Conditions of air are 0.3m³,101kPa, 30C and of nitrogen 0.1³,101kPa,30C. Air is compressed 'till the temperature reaches 200C. Determine:
1)The final pressure of nitrogen
2) The amount of heat transfer between them
3) The work done on the air
4)The value of n if the compression of air follows PVⁿ= Constant.

Homework Equations

Ideal gas law, PV^k=Constant
Q-W=U

The Attempt at a Solution

Since the piston is insulated, the side containing nitrogen has no net transfer of heat towards the surroundings i.e. adiabatic process.
For Nitrogen $\gamma = \frac{c_p}{c_v}= \frac{1.039}{0.743}$
$$P_1V_1^{\gamma}=P_2V_2^{\gamma}$$

$$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$

Combing these two equations I get:

$$T_1V_1^{\gamma -1}=T_2V_2^{\gamma-1}$$
$$\Rightarrow V_2=\frac{T_1}{T_2}V_1^{\gamma-1}$$
$$V_2=\frac{273+30}{273+200}(0.3)^{1.398-1}$$
$$V_2=0.397m^3$$

$$P_1V_1^{\gamma}=P_2V_2^{\gamma}$$
$$\Rightarrow P_2=P_1(\frac{V_1}{V_2})^{\gamma}=68.27kPa$$

2) Work done on N₂

$$W= \frac{P_2V_2-P_1V_1}{1- \gamma}=8.03kJ$$

(this means that the work done by the air on the N₂ is also 8.03kJ)

Now [itex]\delta U=mc_v \delta T[/tex]<br /> <br /> $$m=\frac{P_2V_2}{RT_2}$$<br /> <br /> I was given M=25kg/kmol and I know that MR=r where r is the universal gas constant (8.3143kJ/kgK)<br /> such that R=8.3143/(28x10^-3)=296.94kJ/kg<br /> <br /> $$\delta U= 0.00019kJ$$<br /> (I think my units may be wrong here)<br /> <br /> So then by the 1^st law of thermodynamics, the heat transfer between air and nitrogen is <br /> Q=0.00019+8.03=8.03019kJ.<br /> <br /> This somehow seems wrong to me.[/itex]

 

[Redbelly98]

I haven't checked though your entire derivation, but from reading the problem statement it seems that:

For the nitrogen, there is heat transfer (from the compressed air), but no work (volume=constant).

For the air, there is both work (from compression) and heat transfer (to the nitrogen).

The energy added to the whole system is the work done by the piston, so you can figure out what that is from the temperature rise and amount of each gas present.

The energy added to the nitrogen is the heat exchanged between the two gases. One can figure out what that is from the temperature rise and the amount of nitrogen present.