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Qmechanic ♦
Qmechanic ♦
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Why can we change dt$dt$ with $(dt/dp)_s dp$?

In my homework assignment there's the following question:

a general thermodynamic system is being compressed isentropically from pressure $P_i$ to $P_f$ while keeping the number of particles constant. write down the temperature change of the system using an integral. reduce the partial derivative in the integrand to the measurable quantities: T,V,$\alpha$, $C_p$.

A general thermodynamic system is being compressed isentropically from pressure $P_i$ to $P_f$ while keeping the number of particles constant. write down the temperature change of the system using an integral. reduce the partial derivative in the integrand to the measurable quantities: $T,V,\alpha$, $C_p$.

The solution to the question is the following:

enter image description here

My question is: What was used in the transition from $\Delta$T$\Delta T$ to the first integral over dp$dp$? how would one approach this question and get the correct result as seen above?

Why can we change dt with $(dt/dp)_s dp$?

In my homework assignment there's the following question:

a general thermodynamic system is being compressed isentropically from pressure $P_i$ to $P_f$ while keeping the number of particles constant. write down the temperature change of the system using an integral. reduce the partial derivative in the integrand to the measurable quantities: T,V,$\alpha$, $C_p$.

The solution to the question is the following:

enter image description here

My question is: What was used in the transition from $\Delta$T to the first integral over dp? how would one approach this question and get the correct result as seen above?

Why can we change $dt$ with $(dt/dp)_s dp$?

In my homework assignment there's the following question:

A general thermodynamic system is being compressed isentropically from pressure $P_i$ to $P_f$ while keeping the number of particles constant. write down the temperature change of the system using an integral. reduce the partial derivative in the integrand to the measurable quantities: $T,V,\alpha$, $C_p$.

The solution to the question is the following:

enter image description here

My question is: What was used in the transition from $\Delta T$ to the first integral over $dp$? how would one approach this question and get the correct result as seen above?

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DAcheese
DAcheese
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Why can we change dt with $(dt/dp)_s dp$?

In my homework assignment there's the following question:

a general thermodynamic system is being compressed isentropically from pressure $P_i$ to $P_f$ while keeping the number of particles constant. write down the temperature change of the system using an integral. reduce the partial derivative in the integrand to the measurable quantities: T,V,$\alpha$, $C_p$.

The solution to the question is the following:

enter image description here

My question is: What was used in the transition from $\Delta$T to the first integral over dp? how would one approach this question and get the correct result as seen above?