Just A Couple Of Thermodynamics Questions

[mmmboh]

Please help! I have an assignment due tomorrow, and there are two parts of questions that I cannot get :S

Homework Statement

A substance has an isothermal compressibility of k=-a/v and an expansivity B=2BT/v, where "a" and 'b" are constants. The equation of state is v-bT²+aP=constant (I found this equation)...If at a pressure P₀, and temperature T₀, the specific volume is V₀, evaluate the constant.

2.We have a graph of compressibility and expansivity of copper as functions of temperature at a constant pressure of 1 atm, and the question asks to find the expansivity of copper at 1000 K and 1 atm, and compute the fractional change in volume of the copper when the pressure is isothermally increased to 1000 atm. Assume dB/dT is independent of pressure.

The Attempt at a Solution

I have tried so many thing and I can't figure out what to do! Can someone PLEASE help??

Thank you!

 

[jbsteele]

1. To evaluate the constant, you need to plug in the values of P0, T0 and V0 into the equation of state. This will give you the constant value. 2.From the graph, you can determine the expansivity of copper at 1000 K and 1 atm. You can then use the equation for isothermal compressibility (k=-a/v) and the equation for expansivity (B=2BT/v) to calculate the fractional change in volume of the copper when the pressure is increased to 1000 atm.

 

[kerimek]

Dear student,

I understand that you are struggling with a couple of thermodynamics questions for your assignment due tomorrow. First, let's address the equation of state given in the first part of the question. This equation relates the pressure, temperature, and specific volume of a substance and can be used to calculate the constant in the equation. To do this, we can substitute the given values of P0, T0, and V0 into the equation and solve for the constant.

For the second part of the question, we are given a graph of compressibility and expansivity of copper at a constant pressure of 1 atm. To find the expansivity at 1000 K and 1 atm, we can use the graph to determine the value of B at 1000 K. Then, we can use the given equation B=2BT/v to calculate the expansivity at 1000 K and 1 atm.

To compute the fractional change in volume of copper when the pressure is isothermally increased to 1000 atm, we can use the given equation for the isothermal compressibility, k=-a/v. We know that the compressibility is independent of pressure, so we can use the given value of k to calculate the change in volume when the pressure is increased to 1000 atm.

I hope this helps you to solve these questions. If you are still having trouble, I would recommend seeking help from your professor or a tutor. Good luck with your assignment!