Question

hence obtain it's corresponding forms for an adiabatic process and isothermal process

Answer 1

corresponding form for an adiabatic and tsothermal process is $T^{n-1} = constant$

Explanation: Suppose that the temperature of an ideal gas is held constant by keeping the gas in thermal contact with a heat reservoir. if the gas is allowed to expand quasi statically under these so called isothermal conditions  then the ideal equation of state tells us that pV= constant

this is usually called the isothermal gas law.

according to the first law of thermodynamics,

                           dQ= v$c_v$ dT+pdV=0

in an adiabatic process. the ideal gasc equation of state can be differentiated,

                            pdV+Vdp=vRdT

the temperature increment dT can be eliminated between the above two expressions to give

                   $0= \frac{c_{v} }{R} (pdV+Vdp)+pdV = (\frac{c_{v} }{R} }+1)pdV+\frac{c_{v} }{R}Vdp$

which reduces to      $(c_{v} +R)pdV+c_{v} VdP =0$

dividing through by $c_{v}$pV yields

                   γ$\frac{dv}{V} +\frac{dp}{p} =0$

it turns out that $c_{v}$ is a very slowly varying function of temperature in most gases.

γ$T^{n-1} = constant$

Answer 2

An isothermal process is a change of a system, in which the temperature remains constant, (ΔT = 0).In contrast, an adiabatic process is where a system exchanges no heat with its surroundings (Q = 0).

Explanation:

• Changes of state or phase changes of different liquids through the process of melting and evaporation are examples of the isothermal process.
• One of the examples of the industrial application of the isothermal process is the carnot engine.
• A refrigerator works isothermally.
• An example of an adiabatic process is the vertical flow of air in the atmosphere.
• Air expands and cools as it rises, and contracts and grows warmer as it descends.
• Another example is when an interstellar gas cloud expands or contracts.
• Adiabatic changes are usually accompanied by changes in temperature.

To Learn More...

1.Why is adiabatic curve more steeper than isotherm curve?

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