How To Solve a Problem of Thermodynamics Includes Thermodynamic Graph?

Someone has asked me this question on Quora. I would like to share it with u. Let’s solve it.

Consider following image.

ANSWER :

i)                      Here as we can see in a picture there is the graph of INTERNAL ENERGY (U) ---->PRESSURE P)  is given. Now, consider that this process is constant volume process. So we can write an equation of internal energy like below:

U = m C_V (T₂-T₁)

 Now if the process is not constant volume then there will be C instead of C_v. So, in any case, internal energy will always be related to TEMPERATURE. So we can say that INTERNAL ENERGY IS FUNCTION OF TEMPERATURE.

So, we can consider above graph as TEMPERATURE (T) ---> PRESSURE (P) GRAPH. As shown as below.

Now from a graph, u can say that process “ AC is isothermal process”; “BC is isobaric process”... Now in the case of AB process, its figure is straight which shows that pressure increases with increase in temperature and decreases with a decrease in temperature so basically for AB process P α T  WHICH IS CONDITION FOR ISOCHORIC PROCESS.

SO PROCESS AB IS ISOCHORIC PROCESS and answers B is the right answer.

ii)                  Now for the second problem, as shown in image all options have VOLUME(V) ------> TEMPERATURE(T) graph.

Now as we see in an answer(i), process AB is an isochoric process which can be represented by V ---> T as shown as below:

And as per answer(i), process CB is an isothermal process which can be represented by V ---> T as shown as below:

Now process BC is an isobaric process ( as per answer i ). A condition for an isobaric process is that “VαT” ( from ideal gas equation PV=mRT, in which for isobaric process P, R & m are constants). This means V increases with increasing of T and decreases with decreasing of T (linear relationship between V & T). So on V ---> T diagram process can be represented as:

So, if we combine three images.

 We can say that ANSWER C is the right answer.