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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# 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 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.