Gas expansion at constant pressure

[wavingerwin]

Homework Statement

2 moles of gas at 300 K at 0.02 m³ is expanded to twice the original volume at constant pressure, and then adiabatically until T = 300 K again.

assume monatomic gas. assume ideal.

determine the final volume

determine the heat supplied to the overall process

determine change in internal energy

Homework Equations

$$PV = nRT$$
$$TV^{\gamma-1} = TV^{\gamma-1}$$

The Attempt at a Solution

State 1
n = 2
V = 0.02
R = 8.31
T = 300

P = 249.3 kPa

State 2
P = 249.3
V = 0.04

T = 600 K

State 3
T = 300
monatomic therefore $$\gamma=5/3$$

V = 0.061

so final volume is 0.061 m³

I am struggling to find the "heat supplied" to the system. Since from state 2 to 3 the process is adiabatic, Q = 0.

So the only heat transfer occur from state 1 to 2.

Would it just be equal to the work?
so Q = W = P(V₂-V₁) = 249300 x 0.02 = 5 kJ?

and so the change in internal energy must also be be 5 kJ?

thank you in advance.

 

[ehild]

How can you make the gas expand at constant pressure?

ehild

 

[wavingerwin]

Hi ehild

by applying heat and raising its temperature.

However, I don't have/know an equation that equates total heating applied (Q) to the raise in temperature..

 

[ehild]

What about specific heat capacity at constant pressure?

ehild

 

[wavingerwin]

specific heat, c would equal du/dT

so I guess the heat supplied, q, would equal change in u = c dT

but c is not given in the question.

 

[ehild]

It is 2 moles of mono-atomic ideal gas. Look after cp.

ehild