What can you say about U, Q and W for the following processess? (a) A chemical r

Question

What can you say about U, Q and W for the following processess?

(a) A chemical reaction occurs irreversibly in a well-insulated bomb. There is an increase in the number of mols such that pressure increases considerably. (Please take the bomb as your system)

(b) One kmol of an ideal gas (Cpm=30kJ/kmolK), Cvm=21.7kJ/kmolK) undergoes a process where its temperature changes from 290 to 340 K. The gas volume is the same at the beginning and the end of the process, although during the process the volume may change. (please take the gas as your system)

(c) One kmol of the preceding gas expands irreversibly and adiabatically between P=10bar, T=400K and P=1 bar, T=200K (please take the gas as your system)

Explanation / Answer

What can you say about U, Q and W for the following processess?
(a) A chemical reaction occurs irreversibly in a well-insulated bomb. There is an increase in the number of mols such that pressure increases considerably. (Please take the bomb as your system)
(b) One kmol of an ideal gas (Cpm=30kJ/kmolK), Cvm=21.7kJ/kmolK) undergoes a process where its temperature changes from 290 to 340 K. The gas volume is the same at the beginning and the end of the process, although during the process the volume may change. (please take the gas as your system)
(c) One kmol of the preceding gas expands irreversibly and adiabatically between P=10bar, T=400K and P=1 bar, T=200K (please take the gas as your system)

Solution:-

a) First of all we should make clarity about the U, Q and W . Here, U is change in energy, Q is increase/decrease in the internal energy and W is the work done on the system
From the first Law of Thermodynamics we know that heat added to a system can be given as following:

           U= Q+ W,                   (1)
Where            W= -P V (if required)           (2)

if we put W in equation (1) we get:-

           U= Q - P V,               (3)      
Now if the pressure is increased as a result W which is work done will also increase where as the U will decrease

b) here we are given the values for specific heat and pressure at constant volume:
Cpm=30kJ/kmolK), Cvm=21.7kJ/kmolK
we know that the     nC(v) = ( U/ T),               (4)

(where n=1)

putting the given values in the above equation we get:
           T=340-290=50K
           U= not given

           21.7=( U/50)
   or       21.7*50= U
   or       U=1085KJ

further considering the equation 2, given above we know that the change in volume ( V) in this case is constant so change in volume ( V)=0
           W= -P V now putting the V=0
           W=0
Now considering equation 1, we get
           U= Q+ W,
we know U and W, putting W=0 in above equation
we get,        U= Q,
C) Since the process is adiabetic

           dQ=0,
           U= - W,
   therefore,    U= C(v)*T,
           U= 21.7*200,
           U= 4340KJ,

and W= -(C(v)*T), so whole of internal energy will be observed as the work done.

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