Heat Capacity Ratio

To find C_P/C_V of a gas, one sometimes uses the following method. A certain amount of gas with initial temperature T₀, pressure P₀, and volume V₀, is heated by a current flowing through a platinum wire for a time t. The experiment is done twice: first at a constant volume V₀ with the pressure changing from P₀ to P₁, and then at a constant pressure with the volume changing from V₀ to V₁ The time t is the same in both experiments. Find the ratio C_P/C_V (the gas may be considered ideal).

SOLUTION

If the gas is heated at constant volume, then the amount of heat Q transferred to the gas is

(1)

where c_v is the heat capacity by weight of the gas, m is the mass, and T is the temperature at pressure P₁. Using the ideal gas law at the beginning and end of heating gives

(2)

where n is the number of moles of the gas. From (1) and (2),

(3)

and

(4)

For heating at constant pressure,

(5)

Similarly,

(6)

So

(7)

and

(8)

Since the time t during which the current flows through the wire is the same in both experiments, the amount of heat transferred to the gas is also the same: Q' = Q. Equating (4) and (8), we obtain

(9)

مواضيع ذات صلة

مصطلحات الفيزياء النووية

إزاحة حمراء REDSHIFT

المركبات النانوية (Nanocomposites)

مولد فان دي جراف الالكتروستاتي

التطويرات التقنية الحديثة في المعجلات الالكتروستاتية

معجلات الالكترونات الالكتروستاتية

معجلات الفان دي جراف الترادفية

الحد من زيادة الطاقة في معجل فان دي جراف

أنبوبة التعجيل قي معجلات الجسيمات من نوع فان دي جراف

ارتكاز معجل فان دي جراف

مبدأ تشغيل معجل الفان دي جراف

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