# Thermodynamics I

Fire syringe For an isothermal process, temperature remains constant i.e. it does not change. In essence, the internal energy remains constant and hence the change in internal energy is given as,
This implies that for an isothermal process, if a given amount of heat Q is added to the gas under compression, and equal amount of work, W will be done by the compressed gs on its surrounding. This is represented as show below,
In this scenario, heat flows into the cylinder at a temperature, T resulting into isothermal expansion of the fluid which does work on the piston (Baylin 21). Assume an ideal gas compressed from 300K, 0.1 Mpa to 0.8MPa isothermally. The values of interest will be,
Solving for these values isothermally, no temperature change is expected and hence initial temperature will be equal to final temperature while pressure will change from 0.1Mpa to 008Mpa.
It is presumed that,
For an ideal gas,
The scenario describes isothermal process
In adiabatic expansion, there is rapid compression of the gas resulting increase in temperature. The quick compression denies the system time exchange heat between air within and that in the surrounding. Conventionally, if it was isothermal, when work is done to the fluid, it would have had to corresponding work to the surrounding environment (Baylin 21). This is however not the case in adiabatic. By definition, for any adiabatic process, the following condition should be met,
For an ideal gas,
Consequently,
Borrowing from molar specific heat relations,
And hence, we get,
Ultimately,
Implying a change in temperature for adiabatic. Consequently, adiabatic process will light the paper on fire.
For a tissue paper 1 cm3, targeting combustion of paper at, the following calculations are derived,
Given the compression is adiabatic,
The volume is assumed to decrease rapidly by a factor of 15,
Specific heat capacity of paper =
Assuming initial temperature is 300K,
Given the point of paper’s combustion at 723K, the syringe will ignite the paper
Assuming the tissues lights up when it comes into contact with the piston and that the volume of the cylinder is 1ml, 5 ml, then the volume of the paper will be given as, . This gives 0.3333. Given the paper is 1 cubic centimeter. its thickness will also be 0.3333 cm.
Work Cited
Bailyn, Mark. A Survey of Thermodynamics. New York: American Institute of Physics Press, 2006: 21
Heat flows into cylinder at temperature TH. The fluid expands isothermally and does work on the piston.
The fluid continues to expand, adiabatically.
Work is done by the piston on the fluid, which undergoes an isothermal compression.
The fluid returns to its initial condition by an adiabatic compression.

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