by the way, how can you tell if work is 0 for 2 mol of solid iron (C = 25:1 J/(molK)) is heated from 20C to 200C. How much does its internal energy change?
To determine the work done when heating the solid iron from 20°C to 200°C, we will use the equation:
Work = ∆U - Q,
where ∆U represents the change in internal energy and Q represents the heat transferred. Since the question states that the work is 0, we can simplify the equation to:
0 = ∆U - Q.
This means that the change in internal energy (∆U) is equal to the heat transferred (Q). Therefore, to find the change in internal energy, we need to calculate the heat transferred.
To calculate the heat transferred, we can use the equation:
Q = n * C * ∆T,
where Q is the heat transferred, n is the number of moles, C is the molar heat capacity, and ∆T is the change in temperature.
Given:
n = 2 mol,
C = 25.1 J/(mol*K),
∆T = 200°C - 20°C = 180 K.
Plugging these values into the equation, we can calculate the heat transferred (Q):
Q = 2 mol * 25.1 J/(mol*K) * 180 K = 9024 J.
Since work (W) is 0, we know that ∆U = Q:
∆U = 9024 J.
Therefore, the change in internal energy (∆U) when heating 2 moles of solid iron from 20°C to 200°C is 9024 J.