One mole of an ideal monatomic gas performs a process whose chart in VT coordinates completely lies on a straight line. The heat capacity of the gas at the point A , equidistant from the points of int

Question

One mole of an ideal monatomic gas performs a process whose chart in VT coordinates completely lies on a straight line. The heat capacity of the gas at the point A , equidistant from the points of intersection of the process line with the coordinate axes, is : (Take R = 8.3 J/ ( mol ⋅ K ) )

TestHub · Accepted Answer

The process is a straight line in the V-T plane:

$\frac{V}{V _{0}} + \frac{T}{T _{0}} = 1 \Rightarrow \frac{d V}{d T} = - \frac{V _{0}}{T _{0}}$

At point A (midway between the intercepts): $V = \frac{V _{0}}{2}, T = \frac{T _{0}}{2}$

For 1 mole of ideal gas: $P = \frac{RT}{V} = \frac{R ( T _{0} /2 )}{V _{0} /2} = \frac{R T _{0}}{V _{0}}$

Heat capacity for the process:

$C = \frac{δ Q}{d T} = C_{V} + P \frac{d V}{d T}$

$C = \frac{3 R}{2} + \frac{R T _{0}}{V _{0}} (- \frac{V _{0}}{T _{0}})$

$= \frac{3 R}{2} - R = \frac{R}{2}$

$C = \frac{8.3}{2} = 4.15 J/mol \cdot K$

Physics - Heat & Thermo Question with Solution | TestHub

Doubts & Discussion