What Are the Steps to Solve a Thermodynamics Piston Problem?

[Denn]

Homework Statement

A vertical cylinder with a heavy piston contains air at 285 K. The initial pressure is 3.25 105 Pa, and the initial volume is 0.425 m3. Take the molar mass of air as 28.9 g/mol and assume
CV = 5/2R.

(a) Find the specific heat of air at constant volume in units of J/kg · °C.
J/kg · °C.

(b) Calculate the mass of the air in the cylinder.
kg

(c) Suppose the piston is held fixed. Find the energy input required to raise the temperature of the air to 675 K.
kJ

(d) Assume again the conditions of the initial state and assume the heavy piston is free to move. Find the energy input required to raise the temperature to 675 K.
kJ

Homework Equations

So far I've identified ill need to use these equations:

-Q=m*C*deltaT
-c=Q/m*deltaT
-W=-P(Vf-Vi) (For a isobaric process)
-Q=n*Cv*deltaT (For a gas with constant volume)
-Q=n*Cp*deltaT (For a gas with constant pressure)
-PV=nRT
- Cp-Cv=R

The Attempt at a Solution

To begin i equated the first and the second equation to recieve:
C=n*Cv/m

Mass is the unknown quantity and now I'm stuck.

If the piston is held in place then the volume is constant and the process is isovolumetric and therefore Eint=Q and does Q = n*Cv*deltaT?

If the piston is allowed to move freely then the process is isobaric and the Work = -P(Vf-Vi). Does Eint therefore = Q + W = n*Cp*deltaT - P(Vf-Vi) ?

Any help is greatly appreciated!

Thanks

 

[Andrew Mason]

Homework Statement

A vertical cylinder with a heavy piston contains air at 285 K. The initial pressure is 3.25 105 Pa, and the initial volume is 0.425 m3. Take the molar mass of air as 28.9 g/mol and assume
CV = 5/2R.

(a) Find the specific heat of air at constant volume in units of J/kg · °C.
J/kg · °C.

(b) Calculate the mass of the air in the cylinder.
kg

(c) Suppose the piston is held fixed. Find the energy input required to raise the temperature of the air to 675 K.
kJ

(d) Assume again the conditions of the initial state and assume the heavy piston is free to move. Find the energy input required to raise the temperature to 675 K.
kJ

Homework Equations

So far I've identified ill need to use these equations:

-Q=m*C*deltaT
-c=Q/m*deltaT
-W=-P(Vf-Vi) (For a isobaric process)
-Q=n*Cv*deltaT (For a gas with constant volume)
-Q=n*Cp*deltaT (For a gas with constant pressure)
-PV=nRT
- Cp-Cv=R

The Attempt at a Solution

To begin i equated the first and the second equation to recieve:
C=n*Cv/m

Mass is the unknown quantity and now I'm stuck.

Is the initial pressure supposed to be 325 KPa?

You can calculate the mass from the number of moles, n. You can determine n simply by using the ideal gas equation: n = PV/RT

If the piston is held in place then the volume is constant and the process is isovolumetric and therefore Eint=Q and does Q = n*Cv*deltaT?

Yes. Isochoric = constant volume.

If the piston is allowed to move freely then the process is isobaric and the Work = -P(Vf-Vi). Does Eint therefore = Q + W = n*Cp*deltaT - P(Vf-Vi) ?

If P is constant, the heat flow is: $\Delta Q = nC_p\Delta T$. This takes into account the work that is done since Cp = Cv+R and PdV = nRdT. So in applying the first law for isobaric process:

$$\Delta Q = \Delta U + P\Delta V = nC_v\Delta T + nR\Delta T= n(C_v+R)\Delta T = nC_p\Delta T$$

AM