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Chapter 6: Problem 18

The work done to compress a gas is \(74 \mathrm{~J}\). As a result, \(26 \mathrm{~J}\) of heat is given off to the surroundings. Calculate the change in energy of the gas.

Short Answer

Expert verified
The change in energy of the gas is \(48 \mathrm{~J}\).

Step by step solution

01

Identifying the given quantities

Let's identify the quantities we are given. We are told that the work done to compress the gas is \(74 \mathrm{~J}\) (J for Joules, the unit for work and energy). Furthermore, the gas gives off \(26 \mathrm{~J}\) of heat energy to its surroundings.
02

Understanding the energy conservation principle

The energy conservation applies, which means any work done on the gas goes into increasing its internal energy or is lost as heat energy. The formula to use for the change in energy of the gas is the work done minus the heat given off. The formula is \(\Delta E = W - Q\), where \( \Delta E \) is the change in energy, \(W\) is the work done, and \(Q\) is the heat energy given off. The energy units in this problem are Joules.
03

Calculating the change in energy

To find the change in energy of the gas, we substitute the given values into the equation: \(\Delta E = 74 \mathrm{~J} - 26 \mathrm{~J}\). This simplifies to \(\Delta E = 48 \mathrm{~J}\). So the change in energy of the gas is \(48 \mathrm{~J}\).

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