QuestionJuly 3, 2025

A system gains 772 kJ of heat, resulting in a change in internal energy of the system equal to +211kJ How much work is done?

A system gains 772 kJ of heat, resulting in a change in internal energy of the system equal to +211kJ How much work is done?
A system gains 772 kJ of heat, resulting in a change in internal energy of the system equal to +211kJ How much work is done?

Solution
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Answer

561 \text{ kJ} Explanation 1. Apply the First Law of Thermodynamics The first law states \Delta U = Q - W, where \Delta U is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. 2. Rearrange the Formula to Solve for Work Rearrange to find W: W = Q - \Delta U. 3. Substitute Known Values Substitute Q = 772 \text{ kJ} and \Delta U = 211 \text{ kJ} into the formula: W = 772 \text{ kJ} - 211 \text{ kJ}. 4. Calculate the Work Done Perform the calculation: W = 561 \text{ kJ}.

Explanation

1. Apply the First Law of Thermodynamics<br /> The first law states $\Delta U = Q - W$, where $\Delta U$ is the change in internal energy, $Q$ is the heat added to the system, and $W$ is the work done by the system.<br /><br />2. Rearrange the Formula to Solve for Work<br /> Rearrange to find $W$: $W = Q - \Delta U$.<br /><br />3. Substitute Known Values<br /> Substitute $Q = 772 \text{ kJ}$ and $\Delta U = 211 \text{ kJ}$ into the formula: $W = 772 \text{ kJ} - 211 \text{ kJ}$.<br /><br />4. Calculate the Work Done<br /> Perform the calculation: $W = 561 \text{ kJ}$.
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