Question

What is the difference between isothermal and adiabatic? 300 cm3 of an ideal diatomic gas at a pressure of 1 atmosphere and a temperature of 300 K (i.e. room temperature) is contained by a cylinder with a piston top. A camshaft turns and drives the piston further into the cylinder, reducing the volume to 100 cm3 .

(a) What is the final pressure if this compression takes place isothermally? What is the final pressure and temperature if the compression takes place adiabatically?

(b) Pistons in auto-engine cylinders perform this sort of compression hundreds of thousands of times per minute. Is auto-engine compression more likely to be isothermal or adiabatic?

(c) Which sort of compression would lead to a more efficient engine: isothermal or adiabatic?

Answer 1

When a process happens such that during the process the temperature of system remains constant then this process is called "Isothermal process".

for isothermal process

isothermal process obeys Boyle's law-

On the other hand if a process occurs such that there is no exchange of heat between system and surrounding then process is called "adiabatic process".For adiabatic process-

Adiabatic process obeys Adiabatic equation-

where

(a)Given that-

T1=300k,

V1=300cc

P1=1atm

V2=100cc

If compression takes isothermally then-

If compression is Adiabatic-

for diatomic gas

so-

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(b)Since piston compresses the gas very fast in the engine so that there is very small chance to heat heat exchange between the gas and surrounding so auto engine-compression is more likely adiabatic.

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(C)Adiabatic compression process lead to a more efficient engine because during combustion of the gas we require a high pressure gas at high temperature so that when we ignite it then a high pressure and volume is obtained that pushes the piston with larger force.also adiabatic compression takes very small time compared to isothermal compression so we can make high speed engine only with adiabatic compression.