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College Physics (Urone)
Found in: Page 550

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Short Answer

How much heat transfer occurs from a system, if its internal energy decreased by \({\bf{150}}\;{\bf{J}}\)while it was doing 30.0 J of work?

The amount of heat transferred from the system is \(180\;{\rm{J}}\).

See the step by step solution

Step by Step Solution

Step 1: Given data

Change in internal energy, \(\Delta U = - 150\;{\rm{J}}\)

Work done, \(W = - 30\;{\rm{J}}\)

Step 1: Find an expression to calculate the heat transfer from a system.

According to the first law of thermodynamics, the change in internal energy of a system is equal to the difference of heat transfer occurring in the system and the net work done. It is mathematically expressed as follows;

\(\begin{aligned}{}\Delta U = Q - W\\Q = \Delta U + W\end{aligned}\)

Here,\(\Delta U\)is the change in internal energy, \(Q\)is the net heat transfer and \(W\) is the net work done.

Step 2: Calculate the heat transfer using the given data.

System does the work, hence negetive. The value of the change in internal energy and the work done is given.

\(\begin{aligned}{}\Delta U &= - 150{\rm{ J}}\\W &= - 30{\rm{ J}}\end{aligned}\)

Substituting these values in the expression for heat transfer will give the amount of heat transferred from the system.

\(\begin{aligned}{}Q &= \Delta U + W\\ &= - 150{\rm{ J}} + ( - 30{\rm{ J }})\\ &= - 180{\rm{ J}}\end{aligned}\)

So, \(180\;{\rm{J}}\)of heat is transferred from the system.

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