Thermal Physics Quiz: Air Temperature in a Cabin

Questions and Answers

What does the First Law of Thermodynamics state regarding heat transfer in a closed system?

The total internal energy must decrease over time.

The heat lost by the system equals the heat gained by the surroundings. (correct)

All heat transfer results in work being done on the system.

The internal energy of the system remains constant regardless of heat exchange.

If an ideal gas undergoes a process where no heat exchange occurs, how is the change in internal energy related to work?

The change in internal energy is zero.

The change in internal energy is less than the work done on it.

The change in internal energy is negative regardless of the work done.

The change in internal energy equals the work done on the system. (correct)

During thermal equilibrium, what happens to the temperature of two gases in contact?

Both gases will cool down to absolute zero.

One gas remains at a constant temperature while the other changes.

The temperature will fluctuate until a stable state is reached.

Both gases will reach an intermediate temperature. (correct)

In an insulated system where external work is done, how does the internal energy of the gas change?

It increases by the amount of work done on the gas. Signup and view all the answers

Which condition must be met for a system to be considered adiabatic?

No heat can be exchanged with the surroundings during the process. Signup and view all the answers

What does the first law of thermodynamics state about the relationship between heat, work, and internal energy?

The sum of heat and work is independent of the path taken. Signup and view all the answers

How is the change in internal energy represented mathematically according to the first law of thermodynamics?

ΔE int = Q + W Signup and view all the answers

In a thermodynamic process, what does it mean when Q and W are said to depend on the path taken?

Different processes between the same states can yield different values for Q and W. Signup and view all the answers

Which statement is true regarding the final and initial equilibrium states in a thermodynamic system?

Only specific paths between initial and final states yield a consistent value for Q + W. Signup and view all the answers

What is the implication of an adiabatic process in thermodynamics?

There is no heat exchange between the system and its surroundings. Signup and view all the answers

Study Notes

Cabin Heating Calculation

Cabin dimensions: 6m x 4m x 3m, resulting in a total volume of 72m³.
Contains a 2 kW electric heater.
Assumes perfect airtight conditions; all heat from the heater warms the air.
Aims to determine the time to reach a comfort temperature of 21°C.

First Law of Thermodynamics

The first law states conservation of energy: the heat lost by a hotter gas equals the heat gained by a cooler gas, expressed as Q1 = Q2.
For an ideal gas, internal energy change (ΔE_int) is a result of absorbed heat (Q) and work done (W): ΔE_int = Q + W.
In an adiabatic process (no heat exchange), ΔE_int = dW, leading to the equation ΔE_int = -dW.

Terms of Energy in Thermodynamics

Internal energy change for ideal gases can be represented as ΔE_int = nC_VΔT, where n is the number of moles and C_V is the specific heat capacity at constant volume.
Ideal gas law relates pressure (P), volume (V), and temperature (T): PV = nRT.

Types of Thermodynamic Processes

Adiabatic Process: Insulated system where no heat enters or leaves (dQ = 0).
- Results in work done (W) changing internal energy (ΔE_int = dW).
Isothermal Process: Temperature remains constant (ΔE_int = 0).
- Heat exchange equals negative work done (Q = -W).
Constant Volume Process: No work is done (W = 0).
- All heat absorbed contributes to internal energy (ΔE_int = Q).
Cyclical Process: Returns to the initial state, leading to a net change in internal energy of zero (ΔE_int = 0). Relationship given by Q + W = 0.
Free Expansion: Expansion occurs without external pressure applied, leading to no work done and no heat exchange.

Important Relationships

For any infinitesimal change, the differential form of the first law can be expressed as dE_int = dQ + dW.
In adiabatic processes, changes in pressure and volume can be modeled mathematically to show specific relationships between temperature and volume (T V^(γ - 1) = constant).

Internal Work

In cyclical processes, the net work done can be characterized by the paths taken and whether they are clockwise (work done on the system) or counterclockwise (work done by the system).

Summary

The processes and equations are crucial for understanding how energy is transferred and transformed within thermodynamic systems, particularly in systems involving ideal gases.

Description

This quiz explores the principles of thermal physics and how electric heating affects air temperature in an airtight cabin. Given specific dimensions and heater power, you will calculate the time required for the air to reach a comfortable temperature of 21°C. Test your understanding of ideal gas concepts and heat transfer.