- #1
Titan97
Gold Member
- 450
- 18
Homework Statement
Two adiabatic vessels containing ##n## moles of mono atomic and diatomic gas respectively are connected by a rod of length ##l##, cross sectional area ##A## and thermal conductivity ##k##. The surface of the rod is insulated.
The initial temperatures of the vessels are ##T_1## and ##T_2## respectively. Find the time taken for the temperature difference to be half the initial temperature difference.
Homework Equations
$$\Delta U=nC_v\Delta T$$
##C_{v1}=\frac{3nR}{2}##
##C_{v2}=\frac{5nR}{2}##
The Attempt at a Solution
The gases will undergo an isochoric process. The heat from one vessel moves to the other along the rod.
Heat lost by vessel 1 = heat gained by vessel 2
$$\frac{3}{2}nR(T_1-{T'}_1)=\frac{5}{2}nR({T'}_2-T_2)$$
If the heat energy lost by vessel 1 is ##dQ## in a time ##dt## and the temperature difference is ##\Delta T##,
$$\frac{dQ}{dt}=\frac{\Delta T\cdot kA}{L}$$
But I am not able to continue.
Last edited: