Question

A gas enclosed in a cylinder by means of a piston that can move without friction is warmed, and 1000 J of heat enters the gas. Assuming that the volume of the gas is constant, the change in the internal energy of the gas is a) 0 . b) 1000 J. c) -1000 J. d) none of the above.

Short answer

Question: A gas enclosed in a cylinder is heated, and 1000 J of heat is added to the system. The volume of the gas remains constant. Find the change in internal energy of the gas using the First Law of Thermodynamics. Choose the correct answer among the following options: a) -1000 J b) 1000 J c) 500 J d) 0 J Answer: b) 1000 J

Step-by-step solution

First Law of Thermodynamics

The First Law of Thermodynamics, which is the conservation of energy, states that the change in internal energy of the system ΔU equals the heat added to the system Q minus the work done by the system W. Mathematically, it is represented as: ΔU = Q - W

Identifying the given values and conditions

We are given that 1000 J of heat enters the gas, so Q = 1000 J. Moreover, since the volume of the gas remains constant, this means there is no work done (W = 0).

Applying the First Law of Thermodynamics

Now, let's plug in the given values into the First Law of Thermodynamics equation: ΔU = Q - W ΔU = (1000 J) - (0 J)

Calculating the change in internal energy

By subtracting the work done from the heat entering the gas, we can determine the change in internal energy: ΔU = 1000 J - 0 J ΔU = 1000 J

Identifying the correct answer

Comparing our calculated change in internal energy with the given options, the correct answer is: b) 1000 J

Key concepts

Internal Energy

Internal energy is one of the core concepts in thermodynamics. It refers to the total energy contained within a system, arising from both its kinetic and potential energy of molecules. When discussing thermodynamic processes, particularly those at constant volume, internal energy is crucial because it's what changes as heat is added or removed.

In the given exercise, when heat is introduced into the gas, it causes an increase in the internal energy. This is because the molecules gain kinetic energy from the heat, even though the volume does not change.

The change in internal energy can be calculated using the First Law of Thermodynamics. This law ties it together with heat transfer and work done, establishing that any heat added to the system increases its internal energy if no work is being performed.

Understanding internal energy helps in predicting how a system will behave when subjected to various thermodynamic processes.

Heat Transfer

Heat transfer is the movement of thermal energy from one body or system to another. It occurs due to a temperature difference, and it plays a critical role in changing a system's internal energy.

In the scenario described in the exercise, 1000 J of heat enter the gas. This heat transfer happens at a constant volume, which means that all the heat goes into increasing the internal energy of the gas, rather than doing work by moving the piston.

Heat transfer can happen in three main ways:

• Conduction: Direct contact between particles due to a temperature difference.
• Convection: Movement of fluid, carrying heat energy with it.
• Radiation: Transfer of energy through electromagnetic waves.

In this problem, it is assumed that the heat transfer is directly adding energy into the gas, showcasing the relevance of understanding heat dynamics in thermodynamic processes.

Constant Volume Process

A constant volume process, also known as an isochoric process, refers to a thermodynamic process during which the volume of the system remains unchanged.

In such processes, work done by the system is zero because work involves volume change ( W = P ΔV encompasses volume, thus no volume change means ΔV = 0).

This concept simplifies the application of the First Law of Thermodynamics since the work done term vanishes. Consequently, any heat added to the system directly affects its internal energy.

In the exercise provided, the gas's constant volume means that the complete 1000 J of heat energy is used to increase the internal energy, making problem-solving more straightforward. Understanding constant volume processes is essential for solving many thermodynamic problems, especially involving gases in fixed containers.

Thermodynamics Problem Solving

Solving thermodynamic problems requires understanding and applying various principles and laws correctly. Issues can often be simplified by systematically analyzing given data, identifying knowns and unknowns, and using applicable laws.

In the exercise, the First Law of Thermodynamics is applied to find the internal energy change. The given heat input is first identified, and then it's established that because the volume is constant, no work is done. This simplifies calculating the change in internal energy.

When solving such problems:

• Begin by listing known quantities and what needs to be found.
• Determine which thermodynamic principles apply, like the First Law.
• Consider any constraints, such as constant volume or pressure.
• Plug in the known values into the relevant equations.

Following this structured approach ensures success in thermodynamics problem solving, as demonstrated in determining the correct energy change of 1000 J in the exercise.