19. A cylinder of an ideal gas undergoes a process. It absorbs 10 J of heat in t

Question

19. A cylinder of an ideal gas undergoes a process. It absorbs
10 J of heat in the process.
a) What is the work done by the gas if the process is isothermal ?
What is the qualitative change in pressure ?
b) What is the change of its internal energy if the process
is isochoric ? What is the qualitative change in temperature ?
c) The system of ideal gas is taken through an adiabatic expansion. What is the heat absorbed by the gas in the process ? What is the sign for the work done by the gas during the process ? What is the qualitative change in its internal energy ? What is the qualitative change in temperature ?

Explanation / Answer

We have, q =U +w

a) Since procee is isothermal

so U=nCvT = 0 (asT=0)

heat is absorbed so q will be positive

so, w=10J

Now since temperature is constant,

and wehave , PV=nRT

(with n and R constant)

so if volume decrease(as work done is positive)

Pressure should increase in order to keep nRT constant

b)If process is isochoric, dV=0

so work done =0

so, q=U =10 J

SInce U is positive so final temperature is more than initial temperature.

c) Since the process is adiabatic the heat absorbed during the process = 0J

Since expansion is taking place so work done is negative.

We have

q=U + W

but w is negative and q=0

so U will be positive

SInce U >0

So final temperaturewill be > initial temperature

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