An electrical heater delivers 4.070 kJ of energy (as heat) to a system consisting of the gas inside a cylinder having a movable piston. As a result, the piston moves against a constant external pressure such that P ∆V = 2.442 kJ. What is the change in internal energy for the system?
dE = q + w
q = +4070 J
w = -2442 J
dE = ?
To calculate the change in internal energy for the system, you can apply the first law of thermodynamics, which states that the change in internal energy (∆U) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system on the surroundings.
Mathematically, it can be expressed as:
∆U = Q - W
In this case, the heat added to the system is given as 4.070 kJ (kilojoules). However, you need to determine the work done by the system, which can be calculated using the equation P ∆V, where P is the pressure and ∆V is the change in volume.
Here, it is mentioned that P ∆V equals 2.442 kJ. Note that work is defined as the product of pressure times volume change:
W = P ∆V
Substituting the given values, we have:
W = 2.442 kJ
Now, substitute the values of heat (Q) and work (W) into the first law equation:
∆U = Q - W
∆U = 4.070 kJ - 2.442 kJ
Calculating the difference gives us:
∆U = 1.628 kJ
Therefore, the change in internal energy (∆U) for the system is 1.628 kJ.