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Chapter 12: Problem 99

A gas is compressed from \(600 \mathrm{cm}^{3}\) to \(200 \mathrm{cm}^{3}\) at a constant pressure of \(400 \mathrm{kPa}\). At the same time, \(100 \mathrm{J}\) of heat energy is transferred out of the gas. What is the change in thermal energy of the gas during this process?

Short Answer

Expert verified
The change in thermal energy of the gas during this process is \(60 \, Joules\).

Step by step solution

01

Calculation of Work Done

The work done on the gas can be given by the formula: \( W = -P \Delta V \), where \(\Delta V\) is the change in volume. Here, since the volume decreases (as the gas is being compressed), \(\Delta V = V_f - V_i = 200 - 600 = -400 \, cm^3 = - 4.0 \times 10^{-4} \, m^3\) (note that we have converted cm^3 to m^3). Hence, the work done on the system \( W = -1 \times 400 \times 10^3 \times (-4.0 \times 10^{-4}) = 160 \, J \).
02

Application of the First Law of Thermodynamics

The first law of thermodynamics gives the change in internal energy \(\Delta U\) as the sum of the work done on the gas and the heat added to the gas. Thus, \( \Delta U = W + Q \). In our case, work is done on the gas and heat is removed from the gas, so \( \Delta U=160J - 100J = 60J \).
03

Interpretation of the Result

The change in internal energy, also known as thermal energy in this context, is 60 Joules. This means that even though 100 Joules of heat energy was transferred out of the gas, because 160 Joules of energy was also added to the system through work done on it (compression), there is a net increase in thermal energy.

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