Calculate the change in internal energy (\Delta E) of a system that performs 158 kJ of work on its surroundings and loses 157 kJ of heat. Report your answer with the correct number of significant figures. Do not include units in your answer. Note that internal energy is given the symbol U in some textbooks.

The problem states that the system performs 158 kJ of work and loses 157 kJ of heat.
Apply the first law of thermodynamics: Δ E = q + w .
Substitute the given values: q = − 157 kJ and w = − 158 kJ.
Calculate the change in internal energy: Δ E = − 157 + ( − 158 ) = − 315 kJ. The final answer is − 315 ​ .

Explanation

Problem Analysis We are given that a system performs 158 kJ of work on its surroundings and loses 157 kJ of heat. We need to calculate the change in internal energy ( Δ E ) of the system.

First Law of Thermodynamics The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system plus the work done on the system: Δ E = q + w where q is the heat added to the system and w is the work done on the system.

Determining Heat and Work Since the system loses 157 kJ of heat, the heat added to the system is negative: q = − 157 kJ . Since the system performs 158 kJ of work on its surroundings, the work done on the system is negative: w = − 158 kJ .

Calculating Change in Internal Energy Now, we substitute the values of q and w into the equation for the change in internal energy: Δ E = q + w = − 157 kJ + ( − 158 kJ ) = − 315 kJ .

Final Answer Therefore, the change in internal energy of the system is -315 kJ. Since the question asks for the answer without units, the answer is -315.


Examples
The principles of thermodynamics, such as the one used in this problem, are crucial in designing engines and refrigerators. For example, when designing a car engine, engineers need to carefully consider how much heat is produced and how much work is done by the engine. By understanding the relationship between heat, work, and internal energy, they can optimize the engine's efficiency and reduce its environmental impact. Similarly, in refrigeration, understanding these principles helps in designing systems that efficiently remove heat from a space, keeping it cool.

Answered by GinnyAnswer | 2025-07-05

The change in internal energy ( E) of the system is -315 when it performs 158 kJ of work and loses 157 kJ of heat. Using the formula Δ E = q + w , we find that both heat and work are negative. The final answer, without units, is -315.
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Answered by Anonymous | 2025-07-26