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The quantity that is an exact differential of a state function is (following the convention that heat flowing in and work done on the system are positive)
  • a)
    dq
  • b)
    TdS - PdV
  • c)
    TdS - VdP
  • d)
    VdP + SdT
Correct answer is option 'B'. Can you explain this answer?
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The quantity that is an exact differential of a state function is (fol...
  • Entropy as an exact differential
Because the quantity dS = d′Qmax/T is an exact differential, many other important relationships connecting the thermodynamic properties of substances can be derived. For example, with the subsitution of  d′Q = T dS and d′W = P dV, the differential form (dU = d′Q − d′W) of the first law of thermodynamics becomes (for a single pure substance)
dU = TdS − PdV. 
and dH=TdS+VdP
dG = VdP -SdT
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The quantity that is an exact differential of a state function is (fol...
Explanation:

Exact differential of a state function:
An exact differential of a state function is a quantity that has the property that its integral around a closed loop is zero.

Given options:
a) dq
b) TdS - PdV
c) TdS - VdP
d) VdP + SdT

Explanation of option B:
- TdS is the change in internal energy, PdV is the work done on the system.
- In a reversible process, heat flow is equal to TdS and work done is equal to PdV.
- The combination TdS - PdV represents the change in the energy of the system due to heat and work.
- This combination is an exact differential because it depends only on the initial and final states of the system, not on the path taken.
Therefore, option B (TdS - PdV) is the quantity that is an exact differential of a state function.
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The quantity that is an exact differential of a state function is (following the convention that heat flowing in and work done on the system are positive)a)dqb)TdS - PdVc)TdS - VdPd)VdP + SdTCorrect answer is option 'B'. Can you explain this answer?
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