Thermodynamics and Statistical Mechanics

Q1 In an air compressor the compression takes place at a constant internal energy and

50Kj of heat are rejected to the cooling water for every Kilogram of air. Calculate

the work input for the compression stroke per kilogram of air?

The density of the substance becomes higher because of the particles slow down and move closer together when the substance cools.

The first law is also known as law of conservation of energy. It say that the energy can neither be created nor be destroyed but can only be transferred. Its is given by this equation dQ = dU + dW .

When placed in a flame, the glass bulb expands rapidly. This increases the volume of the bulb and so the column descends. However, the glass then conducts the heat to the mercury so that it undergoes thermal expansion and the column rises.

The transition of a material from liquid to solid invariably involves removing energy from the material. Another way to look at this is that the liquid releases energy as it transitions to being a solid.

A Thermometer is a Closed System.

As from definition any system which can release and except energy but no reduction or increment of mass, is called a closed system.

A thermometer can only take and release energy or heat. But no Mercury vapor comes out from it and neither can we insert any thing.

A polytropic process is a process where ( P ) ( V )^n is maintained throughout the process; commonly a compression or an expansion. The n is called the polytropic exponent and is often between 1.0 and k , the specific heat ratio.

For a reversible, polytropic, and nonflow process :

WB = [ ( P2 ) ( V2 ) - ( P1 ) ( V1 ) ] / [ 1 - n ]

or

WB = [ 1 / 1 - n ][ ( P1 ) ( V1 ] [ ( P2 / P1 )^B - 1 ]

B = ( n - 1 ) / ( n )

For a reversible, polytropic, and steady flow process :

WSF = [ n / 1 - n ] [ ( P1 ) ( V1 )] [ ( P2 / P1 )^B - 1 ]

B = ( n - 1 ) / ( n )

The deformation remaining after a specimen has been stressed in tension for a definite period, and released for a definite period. For creep tests, it is the residual, unrecoverable deformation after the load, causing the creep, has been removed for a substantial and definite period of time.

The law of form, also known as morphology, refers to the study of the structure and shape of living organisms. It encompasses how living organisms are structured and organized at various levels, such as cells, tissues, organs, and overall body plan. Understanding the law of form is crucial for identifying and classifying different species in the field of biology.

In some environments, the vast majority of the biomass of an ecosystem is in upper level predators! (Coral reefs come to mind)

Right, um... The larger predators tend to be more ordered than large numbers of prey. They organize a bunch of little things into one ordered body. As the universe must descend towards disorder, there would typically be more (disorganized) prey than (organized) predators.

An isothermal process takes place at a constant temperature so that the internal energy of a system remains unchanged. For ideal gases, this usually occurs under conditions where heat exchange occurs with the surroundings to maintain a constant temperature.

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. An example of this is when a hot cup of coffee sitting on a table loses heat to the surrounding air, causing its temperature to decrease as the energy is transferred as heat.

The heat required to melt 185 g of ice at 0 C is given by :

QICE = ( mICE ) ( hsfICE ) = ( 185 g ) ( 333.7 J / g ) = 61734.5 J

QW = - QICE = ( mW ) (CshW ) ( - 1.0 C deg )

mW = ( - 61734.5 J ) / ( 4.184 J / g - C deg ) ( - 1.0 C deg )

mW = 14,750 g = 14.75 kg of water <-----

where

mICE is mass of ice

hsfICE is (specific) enthalpy of solid fusion, i.e. enthalpy per unit mass

Cshw is the "heat capacity" of water,

mW is mass of water

NOTE: the literature value for water at °C is actually 4.1858 J/g/°C, so the actual answer should be closer to 14.7485 (not exactly though since the temperature change would be from 15 °C to 14 °C so you would need the heat capacity as a function of temperature over that range, not just the isothermal value at 15 °C). Within the justifiable precision, it still rounds to 14.75 kg, just like the answer above so the error is negligible.

Heat from the sun travels through space to the moon via electromagnetic radiation. When the sun's rays hit the moon's surface, they are absorbed and heat up the surface of the moon. However, the moon has no atmosphere to trap the heat, so temperatures fluctuate drastically between day and night.

The first law of thermodynamics requires that energy input must equal energy output plus energy accumulation. In this case that translates to;

430 J = 120 J + (internal energy change)

so

Internal energy change = 430 J - 120 J = +310 J (the internal energy increased by 310 Joules)

A solar powered air compressor is not a thermodynamic impossibility, but it may be challenging to design a system that efficiently converts solar energy into mechanical energy to compress air. It requires careful engineering to ensure that the system can capture and convert enough solar energy to meet the energy demands of compressing air. Additionally, the intermittent nature of solar energy may require energy storage solutions for continuous operation.

Thermal conductivity depends upon the nature/identity of the substance and upon

temperature. In some cases, such as wood, it depends upon the conduction heat transfer direction with respect to the material structure.

The Ideal Gas Law, equation PV = nRT relates the pressure to the constant R, where P is pressure, V is volume, n is number of moles, and T is temperature.

Boyle's Law provides a relationship between the volume of a gas and its pressure where temperature is constant. The equation is PV = k where P is the pressure of the gas, V is the volume of the gas, and k is a constant.

Charles' law states that the volume of a given mass of a gas, at constant pressure, is directly proportional to its temperature. V1/T1 = V2/T2

The three major modes of heat transfer are conduction, convection, and radiation. Conduction is the transfer of heat through a material by direct contact of particles. Convection involves the movement of fluids or gases to transfer heat. Radiation is the transfer of heat through electromagnetic waves.

1. Airplanes have streamlined shapes to reduce drag and improve aerodynamics.
2. Fish have streamlined bodies to move efficiently through water.
3. Cars often incorporate streamlined designs to enhance fuel efficiency and reduce wind resistance.
4. Speedboats are built with streamlined hulls to glide smoothly through water.
5. Bullet trains have streamlined profiles to decrease air resistance and achieve high speeds.

dU=q-w

where

dU is the differential change in internal energy

q is the differential quantity of heat added to a system

w is the differential quantity of work done by a system on its surroundings

Heat makes things hot.

Usable energy is inevitably used for productivity, growth and repair. In the process, usable energy is converted into unusable energy. Thus, usable energy is irretrievably lost in the form of unusable energy.

No. The second law still determines if a process will take place spontaneously. The first law does not say that if you drop a block of hot iron into a water bath that the iron can't absorb enough energy from the water to melt it while freezing the water as long as the energy absorbed by the iron matches the energy lost by the water. HOWEVER, the second law tells us this won't happen.

The thermal energy change of the system can be calculated using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Therefore, the thermal energy change would be 100 J (heat added) - 60 J (work done) = 40 J.