Is about Statistical mechanics: a) Find the thermodynamic potentials of the ideal gas in its natural...

Is about Statistical mechanics:

a) Find the thermodynamic potentials of the ideal gas in its natural variables, in the representation of energy and entropic. Hint: Make use of the Sackur-etrode equation

b) Is it possible to do the same as in part (a) for Van der Waals gas? Justify your answer mathematically and theoretically.

c) What happens with entropy in systems where some of the thermodynamic variables are intensive. Discuss it for at least two thermodynamic potentials (justify this part mathematically).

Expert Solution

genius_generous answered 1 year ago

The following statements concern a fixed mass of an ideal gas being put through a thermodynamic...

The following statements concern a fixed mass of an ideal gas being put through a thermodynamic process. Which statement is true? A. An isobaric, isothermal process is the same as an isovolumetric, adiabatic process. B. During any isothermal process, no transfer of heat takes place. C. The internal energy of the gas is unchanged by any adiabatic process. D. In an isovolumetric process, if a gas absorbs heat its pressure decreases. E. During isothermal compression, the gas absorbs heat from...

Carbon Emissions from Natural Gas: Worldwide combustion of methane, CH4 (natural gas), provides about 10.9 ×...

Carbon Emissions from Natural Gas: Worldwide combustion of methane, CH4 (natural gas), provides about 10.9 × 1016 kJ of energy per year. If methane has an energy content of 39 × 103 kJ/m3 (at STP: Standard Temperature and Pressure), what mass of CO2 is emitted into the atmosphere each year? Also express that emission rate as metric tons of carbon (not CO2) per year. A metric ton, which is 1,000 kg is usually written as tonne to distinguish it from...

Taking a gas to be ideal and confined to a rigid metal box, find an expression...

Taking a gas to be ideal and confined to a rigid metal box, find an expression for how quickly the mean free path of said gas changes if the temperature is dropping cubically with time (T=T0- At^3) If the initial pressure of the gas is 105 Pa, the intermolecular radius is 2 Ångström, and the initial temperature is 325 K and drops 1 K in the first second, what is the rate of change of the mean free path with...

One of the easiest applications of the ideal gas law is to find the unknown value,...

One of the easiest applications of the ideal gas law is to find the unknown value, given all the others. 6.2 liters of an ideal gas are contained at 3.0 atm and 37 °C. How many moles of this gas are present?

For the following, assume air is an ideal gas with constant specific heats at 300K. Find...

For the following, assume air is an ideal gas with constant specific heats at 300K. Find the work and heat transfer and state whether they are into or out of the air. In an open system, air is heated at constant pressure from 27°C, 400 kPa to 500K. w = 0 kJ/kg, q = 201 kJ/kg In a closed system, air is heated at constant pressure from 27°C, 100 kPa to 500K. w = 57.4 kJ/kg, q = 201 kJ/kg

An ideal gas has a constant volume specific heat cv as a function of temperature. Find...

An ideal gas has a constant volume specific heat cv as a function of temperature. Find the change in internal energy and enthalpy if the gas is heated from a temperature of 300K to 600K. cv(T) = 716.66 + 0.4T + 0.000667T2 J/kg.K Also, sketch the constant pressure specific heat as a function of temperature and mention the point T = 400K on the cp – T diagram. Assume that the gas constant of the given ideal gas is 286.9...

Find the Gibbs free energy for G(T,P) for an ideal gas with constant cv.

It’s September 2015 and Apache is about to acquire a natural gas reserve at a price...

It’s September 2015 and Apache is about to acquire a natural gas reserve at a price which translates to $1.75 per thousand cubic feet of reserves. It wants to establish a costless collar for January 2016 sales of 500B cubic feet of natural gas, using January put and call options. One option contract is for 10,000 mmBtus, where mmBtu denotes 1 million British thermal units. Puts with a strike of $2.85/mmBtu have a premium of $0.168/mmBtu, while calls with a...

1a. What happens to the pressure of an ideal gas if you double its temperature in...

1a. What happens to the pressure of an ideal gas if you double its temperature in a closed volume? And what happens to the pressure of an ideal gas if you double its volume at a fixed temperature?Please explain your answer using the combine gas law. 1b. Based upon the standard molar volume, what volume would 0.500 moles of an ideal gas occupy at STP? And based upon the standard molar volume, what volume would be occupied by 1.00 mol...

Think about the assumptions involved in the ideal gas law and kinetic molecular theory. For each...

Think about the assumptions involved in the ideal gas law and kinetic molecular theory. For each pair below determine which system is more likely to obey the ideal gas law and explain why you made your choice. A one liter container of Xe at 760 torr and 273 K or A one liter container of He at 760 torr and 273 K? A one liter container of He at 76.000 torr and 273 K or A one liter container of...

Question