The thermal expansion coefficient and thermal compressibility are defined as alp

Question

The thermal expansion coefficient and thermal compressibility are defined as alpha = 1/V (partial differential V/partial differential T)_P (partial differential ln V/partial differential T)_P beta = -1/V (partial differential V/partial differential P)_T -(partial differential ln V/partial differential P)_T What are the units of alpha and beta? The equation of state, V(P, T), for an ideal gas is V = nRT/P What are the values of alpha and beta for an ideal gas at 1000K and 10^4 Pa? Assume that alpha for a material is a constant and doesn't depend on temperature. Also, it is given that the volume is V_o at a temperature of T_o. Derive an expression for the volume of the material as a function of temperature, V(T).

Explanation / Answer

a) unit of alpha

it is the ratio of fractional change in size of the material to its change in temperature

its units are ok-1 or oC-1

units of beta

it is the ratio of change in size of the material to its change in pressure

its unit are m2/N or Pa-1

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