Deriving an expression for change in internal energy

[Krisd98]

Homework Statement

A quantity of ideal gas initially at 20 atmospheres in a volume of 1 litre and a temperature of 300K suddenly expands and comes to equilibrium with a volume of50 litres and a pressure of 1 atmosphere. If the process is irreversible and involves the transfer of heat and work derive an expression for the difference in the internal energy of the gas

Relevant Equations

du=nc_vdt

Homework Statement: A quantity of ideal gas initially at 20 atmospheres in a volume of 1 litre and a temperature of 300K suddenly expands and comes to equilibrium with a volume of50 litres and a pressure of 1 atmosphere. If the process is irreversible and involves the transfer of heat and work derive an expression for the difference in the internal energy of the gas
Homework Equations: du=nc_vdt

I started of by finding the number of moles using this equation : PV=nRT. I found n=0.802.
I then found the final temperature from this equation: (P_1V_1/nRT_1)=(P_2V_2/nRT_2) and by rearanging found T_2=750K.
I have now constructed a pressure versus volume diagram to calculate the work and change in internal energy.
In the first it the volume is conatant so there's no work done so the internal energy is : change in U=Q
In the second bit the process is isothermal therefore the internal energy =0 but there is work done and Q=+.
Im unsure how to derive an expression for this could someone give me a little hint please

 

[Chestermiller]

How is the internal energy of an ideal gas related to temperature?

 

[Krisd98]

How is the internal energy of an ideal gas related to temperature?

dU=nC_vdT or dU=Q+W

 

[Chestermiller]

dU=nC_vdT or dU=Q+W

From the first equation, if you know the initial and final temperatures, don't you know the change in internal energy per mole?

 

[Krisd98]

From the first equation, if you know the initial and final temperatures, don't you know the change in internal energy per mole?

So i would have dU=0.8*5/2*8.314*750-300)

 

[Chestermiller]

Yes. Please use delta’s and not d’s.