Lecture 20: Thermodynamics - Temperature and Heat 1

Temperature and Heat - Lecture 20

Introduction to Thermodynamics

• Thermodynamics is the study of heat and temperature: their nature, movement, and effects.

• This lecture focuses on defining temperature and discussing its effects.

Temperature Measurement

Temperature Scales

• Temperature is a component in determining heat energy but not the only factor.

• Two common temperature scales:

  • Fahrenheit

  • Celsius (also known as Centigrade pre-1948)

Celsius Scale

• Defined based on the phase changes of water.

  • Steam point: Liquid water turns to vapor (boiling point).

  • Ice point: Liquid water turns to solid (freezing point).

• Ice point is defined as 0°C, and the steam point is defined as 100°C.

• The choice of 0 and 100 is somewhat arbitrary, but convenient for calculations.

Fahrenheit Scale

• Based on a different physical standard than the Celsius scale.

• The ice point (freezing point of water) is 32°F.

• The steam point (boiling point of water) is 212°F.

Scale Differences

• Celsius: 100 degrees between freezing and boiling.

• Fahrenheit: 180 degrees between freezing and boiling (212 - 32 = 180).

• Ratio: 1 Celsius degree = 1.8 Fahrenheit degrees (or 9/5).

• Offset: The Fahrenheit scale is offset by 32 degrees relative to the Celsius scale at the ice point.

Temperature Conversion

Reasoning Strategy for Conversion

• Determine the magnitude difference between the stated temperature and the ice point on the initial scale.

• Convert this number of degrees from the initial scale to the target scale using the conversion factor (1°C = 1.8°F).

• Add or subtract the offset on the new scale to or from the ice point on the new scale.

Fahrenheit to Celsius Conversion Example

• Convert 98.6°F (healthy body temperature) to Celsius.

  1. Determine the difference from the ice point on the Fahrenheit scale: 98.6 - 32 = 66.6 Fahrenheit degrees above the ice point.

  2. Convert Fahrenheit degrees to Celsius degrees: 66.6 \times (5/9) = 37 degrees Celsius above the ice point.

  3. Since 0°C is the ice point on the Celsius scale, the temperature is 37°C.

Celsius to Fahrenheit Conversion Example

• Convert -20°C to Fahrenheit.

  1. Determine the difference from the ice point on the Celsius scale: 20 degrees Celsius below freezing.

  2. Convert Celsius degrees to Fahrenheit degrees: 20 \times (9/5) = 36 Fahrenheit degrees below freezing.

  3. Subtract this from the ice point on the Fahrenheit scale: 32 - 36 = -4°F.

Kelvin Scale

• Important for gas law problems.

• Using Celsius temperatures in gas law equations will yield incorrect results.

Celsius vs. Kelvin

• Steam point:

  • Celsius: 100°C

  • Kelvin: 373.15 K

• Ice point:

  • Celsius: 0°C

  • Kelvin: 273.15 K

• The scales are 100 degrees apart, so 1 Kelvin = 1 Celsius degree.

• Offset: 0°C = 273.15 K.

Conversion Equation

T{Kelvin} = T{Celsius} + 273.15

Absolute Zero

• Zero Kelvin (0 K) is absolute zero, the coldest possible temperature.

• Molecular motion stops at absolute zero.

• Outer space has a temperature of approximately 2.7 Kelvins due to residual radiation from the Big Bang.

Temperature Extremes in Space

• Orbiting Earth, temperatures can range from approximately 75 K (-198°C, -324°F) on the shaded side to 400 K (127°C, 260°F) on the sunny side.

• Spacecraft design must account for expansion and contraction due to these temperature extremes.

Thermometers

Types of Thermometers

• Liquid or gas thermometers

• Thermocouples

• Thermistors

• Thermographs

Liquid and Gas Thermometers

• Liquid thermometers use the expansion and contraction of a liquid in a glass tube to measure temperature.

• Common liquids: mercury or alcohol with dye.

• Gas thermometers operate on the same principle but use a gas.

Thermocouples

• Consist of two wires of dissimilar materials soldered together.

• The junction produces a potential difference (voltage) proportional to temperature.

• Require a microvoltmeter to measure the voltage.

• Bare thermocouples can be used to measure real-time temperatures.

• Thermocouple probes are available for various applications (immersion, piercing, air).

• Thermocouples need to be calibrated for high accuracy.

• Damage to the thermocouple wire can affect calibration. Therefore, must replace it instead of repairing it.

Thermistors

• Measure temperature based on the change in electrical resistance of a material.

• Resistance has a linear and long temperature span.

• Common in inexpensive under-the-tongue thermometers.

• Less accurate than thermocouples (±0.25°C to ±0.5°C).

Thermographs

• Also called infrared thermometers.

• Measure temperature by intercepting infrared radiation emitted by an object.

• Useful for measuring temperatures remotely.

Thermal Expansion

Linear Thermal Expansion

• The phenomenon where the size of an object changes with temperature.

• Increase in temperature leads to expansion, decrease leads to contraction.

• Applies to linear dimensions (length, width, diameter).

• Equation: \Delta L = \alpha L_0 \Delta T

  • \Delta L = Change in length

  • \alpha = Coefficient of linear expansion (per degree Celsius)

  • L_0 = Original length

  • \Delta T = Change in temperature

• The term "linear" refers to the fact that a linear dimension of something gets longer.

• The equation applies to both expansion and contraction, depending on the sign of \Delta T

Coefficients of Linear Expansion

• Different materials have different coefficients of linear expansion.

• Liquids do not have a linear expansion coefficient because they flow and do not expand in a rigid way along a given axis.

• For solids, the volumetric expansion coefficient (\beta) is related to the linear expansion coefficient (\alpha) by: \beta = 3\alpha

Practical Implications of Thermal Expansion

• Materials expand and contract differently.

• Joining materials: engine blocks (cast iron) and heads (aluminum) expand differently.

• Aluminum and glass expand at different rates. If aluminum expands faster, put glass loosely in the hole. However, if temperature goes down, there cannot be excess pressure along the sides. So, use rubber silicone to counter the difference in expansion.

• Expansion joints in concrete sidewalks and structures can prevent cracking.

• Pyrex glass has a low expansion coefficient compared to soda-lime glass, making it more resistant to thermal shock.

• Bimetallic strips: if it's heated up, brass gets larger more per Celsius degree than the steel. If it's cooled down, it gets shorter more per degree than the steel.

Example: Concrete Slab Expansion

• A concrete slab is laid between two buildings. Initially, size fits at 25 degrees Celsius. If the temperature increases to 38 degrees Celsius, the slab expands and buckles.

• Find the buckling (height) by considering concrete expands and becomes a hypotenuse of a right triangle. Adjacent side is initial concrete length, and opposite side is buckle height.

• Temperature change: 13 degrees Celsius, Initial length: 3 meters, Concrete's value for \alpha = 1.0 \times 10^{-5}

• Calculation:

  • Calculate how much the material expanded in meters: \Delta L = \alpha L_0 \Delta T

• The expansion formula is an estimation of increased length. Then, determine the buckle height:

  • Original side is 3 meters.

  • New Side: 3 + \Delta L

  • Hypotenuse = \sqrt{(3)^2 + (\Delta L)^2}.

Bimetallic Strip

• Two metals with different coefficients of thermal expansion, welded together.

• Common combination: brass and steel.

• When heated, the metal with the higher expansion coefficient expands more, causing the strip to bend. If steel has larger expansion coefficient, heat will cause bimetallic strip to bend towards brass.

• Used in thermostats and switches.

• Electromechanical components are durable and inexpensive.

Bimetallic Switch Example

• Used in toasters, coffee makers, and crock pots.

• A bimetallic strip is positioned near a heating element.

• When the strip gets hot, it bends away, breaking the circuit, and turning off the heating element.

• As it cools, it bends back, re-establishing the circuit.

• The shutoff temperature on coffee pot is determined by the position of knob.

Gridiron Pendulum

• Compensated for temperature changes, it consists of the same amount of mass stacked vertically to counteract expansion.

• Uses iron and zinc rods with specific length ratios to maintain a constant pendulum length.

• Compensates by having the rods go up and down each side of pendulum, compensating to keep center axis point in same place.

• A regular pendulum made of iron would gain or lose a quarter of a second per day per degree Celsius of temperature change.

Hole Expansion

• When an object with a hole is heated, the hole expands. Usually, the assumption is that the hole will get smaller. But that is false. Void space surrounded by uniform material is important.

• The hole expands as if it were made of the surrounding material.

• Use the same linear thermal expansion equation to calculate its new dimensions.

Hole Expansion Example: Engagement Ring

• A gold engagement ring (initial diameter = 1.5 x 10^-2 m, temperature = 27°C) falls into hot water (49°C).

• Find the increase in the diameter of the center of the gold ring

• Ring's temperature is equal to the water temperature when it falls into water (49 degrees Celsius).

• Temperature increases from 27 degrees Celsius to 49 degrees Celsius.

• Find its new change in diameter using similar thermal expansion formula.

Volumetric Thermal Expansion

• The change in volume of a substance due to a change in temperature.

• Equation: \Delta V = \beta V_0 \Delta T

  • \Delta V = Change in volume

  • \beta = Coefficient of volumetric expansion (per degree Celsius)

  • V_0 = Original volume

  • \Delta T = Change in temperature

Application: Car Radiator and Coolant Reservoir

• The radiator and coolant have different coefficients of volumetric expansion.

• As the engine heats up, the coolant expands more than the radiator itself.

• The coolant overflows into a reservoir to accommodate the excess volume, and is drawn back into the radiator when it cools.

Example Problem

• Initial temperature is 6 degrees Celsius. Radiator is full, so volume is equal to the initial value, which is 15 quarts. Final temperature is 92 degrees Celsius.

• How much volume does the coolant become to.
  Coolant Expansion: \beta = 410 \times 10^{-6}, \Delta T = 86 degrees Celsius -> \Delta V = 0.53 Quarts.

Radiator Expansion: \beta = 51 \times 10^{-6}, \Delta T = 86 degrees Celsius -> \Delta V = 0.07 Quarts.

• Difference between the two = 0.46. Overflow has to be that much to avoid overflow.

Water Freezing and Pipes

• Water pipes freeze in the winter. And, standard faucet pipes are prone to cracking when pipes don't work by stemming a plunger, but by pushing a washer to a hole to block pressure, a segment of water does not change in volume.

• Ice occupies around 8.3\% more volume, fixed position volume causes breakage.

• To prevent: Wrap Styrofoam cups, wrap a towel around, or other insulation material.

• Long stem faucet: Stem goes along way to disconnect water that goes into pipe that connects to outdoor pipe. Otherwise, use barn valve (a long underground water system).

Quirks about Water at Four Degrees Celcius or About 39 Degrees Fahrenheit

Key Points

• Great for calibrating specific gravity for density, as it can be calibrated. Otherwise, volume goes down in water.

• Maximum density at 4 degrees Celsius. In fact, lakes and rivers freeze from the top down, for a long period.

• Loses heat from the top side, so it gets colder as a result, sinking to the bottom and cycling to a slightly warmer top. This continues to happen until all waters on top are roughly at these parameters. But, for places with a really cold winter, a lot of water may also freeze.

• In the springtime, opposite pattern, temperature stays the same, creating a separation on lake that maintains ecological balance.