Thermal Expansion for an Ideal Gas

[ryaneye]

Homework Statement

The pressure p , volume V, number of moles n, and Kelvin temperature K of an ideal gas are related by the equation pv=nRT , where R is a constant. Prove that the coefficient of volume expansion for an ideal gas is equal to the reciprocal of the Kelvin temperature if the expansion occurs at constant pressure.

Homework Equations

Compare the coefficients of volume expansion of copper and air at a temperature of 20 C. Assume that air may be treated as an ideal gas and that the pressure remains constant.

The Attempt at a Solution

?

 

[TeethWhitener]

The coefficient of thermal expansion at constant pressure is given by
$$\alpha_V=\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_p$$
By calculating this quantity for $V(T)=\frac{nRT}{p}$, you can show an inverse temperature dependence.