Question

A monatomic ideal gas expands slowly to twice its original volume, doing 430 J of work in the process.

A) Find the change in internal energy of the gas if the process is isothermal.

B) Find the heat added to the gas if the process is adiabatic.

C) Find the change in internal energy of the gas if the process is adiabatic.

D) Find the heat added to the gas if the process is isobaric.

E) Find the change in internal energy of the gas if the process is isobaric.

Answer 1

Total heat in a thermodynamic process can be written as

Where, is change in internal energy

is workdone

is total heat change in the process

(A) In isothermal process

Therefore, change in internal energy in this process = 0

(B) In the adiabatic process

Therefore, total heat added in the in the process = 0

(C)

In the adiabatic process the work is done on the cost of change in internal energy. i.e.

or,  

or,

Given,   

therefore,

(D) In isobaric process

  

And for monoatomic gas

Given, the volume gets double slowly in the process.

Let the initial volume of gas was V .

From ideal gas equation we can write,

  

or,   

Therfore, the temperature will also get doubled in the process.

SO, we can write

  

and   

and the workdone ,

or,

From ideal gas equation,

or,

Now,

  

Therefore,

(E)   

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