A reaction at 3.24 atm consumes 5.10 L of a gas adiabatically (q = 0). Calculate the change in internal energy of the system (in kJ).
dE = q+w
dq = 0
w = -p*dV = -p*(V2-V1)
How do I get the V1
v2 is zero
V1 is 5.10L
To calculate the change in internal energy of the system, we need to use the equation:
ΔU = q + w
where ΔU is the change in internal energy, q is the heat transferred to or from the system, and w is the work done on or by the system.
In this case, the question states that the reaction is adiabatic (q = 0), which means no heat is transferred. Therefore, the equation simplifies to:
ΔU = w
Now we need to calculate the work done (w) on the system. The work done in an adiabatic process can be calculated using the formula:
w = -PΔV
where P is the pressure and ΔV is the change in volume.
The question provides the pressure (P) as 3.24 atm and the volume change (ΔV) as 5.10 L. However, to use this formula, we need to convert the pressure from atm to joules.
1 atm = 101.325 J
1 L = 0.001 m^3
So, first, we convert the pressure to joules:
3.24 atm * 101.325 J/atm = 328.122 J
Next, we calculate the work done:
w = -PΔV = -328.122 J * 5.10 L * 0.001 m^3/L = -1.674 J
Finally, we convert the work done from joules to kilojoules:
-1.674 J = -1.674 * 10^(-3) kJ = -1.674 kJ
Therefore, the change in internal energy of the system is -1.674 kJ.