PLEASE SHOW ALL WORK FOR A THUMBS UPSolutionWe know dUTdSPdV

PLEASE SHOW ALL WORK FOR A THUMBS UP

Solution

We know dU=TdS-PdV

so dU/dV=-P---------------------------(1)

and F=U-TS

so dF=dU-d(TS)

dF=TdS-PdV-(TdS+SdT)   .(.by putting the value of dU)

dF=TdS-PdV-TdS-SdT

dF=-PdV-SdT

so dF/dV=-P-------------------(2)

from equation 1and 2 we see that pressure can be expressed as P=(minus)dU/dV and (minus)dF/dV

here we are taking the derivative .so the statement is correct as above proof.