How to find equilibrium temperature of a system

[hunterstein]

Homework Statement

A gas is in an insulated box, which is divided into two portions by an insulated partition. There are n1 moles of the gas at temperature T1 in volume V1, and likewise n2 moles of the (same) gas at temperature T2 in volume V2. The partition is composed of two layers; one layer is insulating (e.g. mashed newspaper) and the other layer is not (e.g., metal). The insulating layer is gently removed, but the non-insulating partition remains. The system is allowed to come to equilibrium.

a) What is the equilibrium temperature of the system?
b) If n1 = n2 what is the equilibrium temperature?
c) Use your result to find the equilibrium temperature for the situation when a small amount of milk is added to very hot tea. More precisely, let = n1/n2 and let δ = T1/T2 and assume that 1 and δ 1. Then expand the expression for the equilibrium temperature to first order in and to first order in δ. You can do this by first expanding in one parameter, then the other.

Can someone help me out with this? Please do not feed me the answer, I need to learn and understand this subject

 

[LunaFly]

Think about it in terms of energy. The system has a certain amount of energy in the form of thermal/kinetic energy. Since it is isolated from the environment the total thermal energy will not change, just redistribute. Does that help?

 

[hunterstein]

Think about it in terms of energy. The system has a certain amount of energy in the form of thermal/kinetic energy. Since it is isolated from the environment the total thermal energy will not change, just redistribute. Does that help?

I was thinking like that, and the first thing that popped into my head is that the equilibrium Temperature would be T1 + T2, but that can't be right

 

[LunaFly]

I was thinking like that, and the first thing that popped into my head is that the equilibrium Temperature would be T1 + T2, but that can't be right

That's not quite right. The temperature of the system isn't a constant. The thermal energy is what's constant. How does the temperature relate to thermal energy? (there is an equation...)

 

[hunterstein]

That's not quite right. The temperature of the system isn't a constant. The thermal energy is what's constant. How does the temperature relate to thermal energy? (there is an equation...)

E= c * m * deltaT? I was thinking that had something to do with it, but specific heat or mass isn't mentioned at all.

 

[haruspex]

E= c * m * deltaT? I was thinking that had something to do with it, but specific heat or mass isn't mentioned at all.

Just think of one of the gas volumes to start with. If a quantity of heat $\Delta Q$ escapes, what remains constant? What is the resulting temperature? If you need to invent an unknown for specific heat, do so. Maybe it will cancel later on.