Question

In an adiabatic compression process, the internal energy of the gas: a. increases because the work done on the gas is negative. b. increases because the work done on the gas is positive. c. decreases because the work done on the gas is negative. d. decreases because the work done on the gas is positive.

Short answer

The internal energy of the gas increases because the work done on the gas is positive (b).

Step-by-step solution

- Understand the adiabatic process

In an adiabatic process, there is no heat exchange with the surroundings. This means that the internal energy change of the gas is due only to the work done on or by the gas.

- Determine the direction of work

During compression, work is done on the gas. In this case, positive work is done on the gas, meaning the energy is being added to the system.

- Relate work to internal energy

According to the first law of thermodynamics, \(\triangle U = Q + W\), where \(\triangle U\) is the change in internal energy, \(Q\) is the heat added to the system (which is zero in an adiabatic process), and \(W\) is the work done on the system. Because \(Q = 0\), the change in internal energy \(\triangle U\) equals \(W\). Therefore, if positive work is done on the gas, the internal energy of the gas increases.

- Choose the correct answer

Based on the analysis, the internal energy of the gas increases because the work done on the gas is positive. Thus, the correct answer is option b.

Key concepts

Adiabatic Compression

In an adiabatic process, a gas is compressed or expanded without exchanging heat with its surroundings. This means that all the energy change within the system comes from the work done on or by the gas. During adiabatic compression, the gas is compressed and work is done on the gas. This work increases the internal energy of the gas since no heat is lost or gained during the process.

Internal Energy

Internal energy is the total energy contained within a system due to the motion and interactions of its molecules. It includes kinetic and potential energy at the microscopic level. When work is done on a gas without any heat exchange, like in an adiabatic process, the internal energy of the gas changes. For adiabatic compression, the internal energy increases because the work done on the gas adds energy to the system.

First Law of Thermodynamics

The first law of thermodynamics is a restatement of the law of energy conservation. It states that the change in internal energy (\triangle U) of a system is equal to the heat added to the system (Q) plus the work done on the system (W): \ \[\triangle U = Q + W\]. In an adiabatic process, no heat is exchanged (Q = 0), so the equation simplifies to: \ \[\triangle U = W\]. Hence, if work is done on the gas (positive W), the internal energy increases.

Work Done on Gas

Work done on a gas involves compressing it by applying a force which decreases the volume of the gas. During adiabatic compression, this work translates directly into an increase in the gas's internal energy because there is no heat exchange. The more work done, the more the energy added to the gas, increasing its internal energy. This relationship is crucial for understanding how energy transformations occur in thermodynamic processes.