A gas is undergoing an adiabatic process. At a certain stage, the volume and absolute temperature of the gas are V 0 , T 0 and the magnitude of the slope of the V-T curve is m . molar specific heat of the gas at constant pressure is [Assume the volume of the gas is taken on the y-axis and absolute temperature of the gas taken on x-axis]

Question

A gas is undergoing an adiabatic process. At a certain stage, the volume and absolute temperature of the gas are V 0 , T 0 and the magnitude of the slope of the V-T curve is m . molar specific heat of the gas at constant pressure is [Assume the volume of the gas is taken on the y-axis and absolute temperature of the gas taken on x-axis], m R T 0 V 0, m R T 0 2 V 0, V 0 + m T 0 R V 0, V 0 + m T 0 R 2 V 0

MARKS App · Accepted Answer

For adiabatic process T V γ - 1 = constant Differentiating with respect to T V γ − 1 + T ( γ − 1 ) V γ − 2 d V d t = 0 ⇒ d V d T = - V T γ - 1 , d V d T T 0 , V 0 = m ⇒ V 0 T 0 γ - 1 = m γ - 1 = V 0 T 0 m C V = R γ - 1 = R T 0 m V 0 C P = C V + R = 1 + T 0 m V 0 R = ( V 0 + m T 0 V 0 ) R

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