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The internal energy of a certain system is a function of temperature alone and is given by the formula E = 25 0.25t kJ. If this system executes a process for which the work done by it per degree temperature increase is 0.75 kJ/K, then the heat interaction per degree temperature increase, in kJ, is?
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The internal energy of a certain system is a function of temperature a...
Given:
Internal energy of the system: E = 25 + 0.25t kJ
Work done per degree temperature increase: 0.75 kJ/K

To find:
Heat interaction per degree temperature increase

Explanation:
The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

Mathematically, it can be expressed as:
ΔU = Q - W

Where:
ΔU is the change in internal energy
Q is the heat added to the system
W is the work done by the system

Since the given internal energy is a function of temperature alone, we can differentiate it with respect to temperature to find the heat interaction per degree temperature increase.

Differentiating the internal energy equation with respect to temperature:
dE/dt = 0.25 kJ/K

Calculating the heat interaction:
By the first law of thermodynamics, we know that ΔU = Q - W

Since the system executes a process for which the work done per degree temperature increase is 0.75 kJ/K, we can substitute the values into the equation:

0.25 kJ/K = Q - 0.75 kJ/K

Solving for Q:
Q = 0.25 kJ/K + 0.75 kJ/K
Q = 1 kJ/K

Therefore, the heat interaction per degree temperature increase is 1 kJ.

Summary:
The heat interaction per degree temperature increase for the given system is 1 kJ.
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The internal energy of a certain system is a function of temperature alone and is given by the formula E = 25 0.25t kJ. If this system executes a process for which the work done by it per degree temperature increase is 0.75 kJ/K, then the heat interaction per degree temperature increase, in kJ, is?
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