First Law of Thermodynamics issue

[ghostops]

Homework Statement

In an experiment to simulate conditions within an automobile engine, 0.155 mol of air at a temperature of 780K and a pressure of 3.20x10⁶ Pa is contained in a cylinder of volume 310 cm³. Then 670 J of heat is transferred to the cylinder.

A) If the volume of the cylinder is constant while the heat is added, what is the final temperature of the air? Assume that the air is essentially nitrogen gas.

B) If instead the volume of the cylinder is allowed to increase while the pressure remains constant, find the final temperature of the air.

Homework Equations

Const P W= pdV Q=nC_pdT
Const V W = 0 Q = nC_vdT
dU = nCdT
C_p = 5/2R
C_v = 3/2R

The Attempt at a Solution

For part A where Volume is constant, it told me that 670 J of heat is added which would be the Q value for dU. so the overall internal energy is 670 J from that I used the equation dU= nC_v(T_f-T_i) which with values came out too 670 = (.155)(3/2*8.314)(T_f-780) which equaled 1126 K. which ended up not being the right answer. I do not know what else to try.

For Part B, I know I need to figure out dU which is Q-W so for this equation it would come out to dU = 670 - pdV or dU = 670 - 3.20E6(V_f-3.1E-4m³). but don't really know where to go from here

 

[Adithyan]

• 
  Nitrogen is a diatomic gas therefore C_v=2.5
  
  For part B, find V_f as you have been finding and then use the ideal gas relation:
  
  PV=nRT
  
  

 

[ghostops]

the Diatomic gas worked, forgot about that tidbit.

but for the Part B I don't fully understand what you mean because I have 2 unknown variables V_f and T_f which is why I am a little lost.

 

[ghostops]

Figured it out thanks!, took a good minute though

 

[Gulab]

Can you please share the workings of the solution

 

[CheyT]

For part b, you use the same equation and everything except that Cv is now Cp, which is just Cv + R.