# Heat Transfer Final Temperature Problem

#### breez

There are two insulated compartments separated by a thin wall. The left side contains .060 mol of He at a initial temperature of 600 k and the right side contains .030 mol He at the initial temperature of 300 K. The compartment on the right is attached to a vertical cylinder, above which the air pressure is 1.0 atm. A 10-cm-diameter, 2.0 kg piston can slide without friction up and down the cylinder. The volumes of the compartments are not known, but the cylinder diameter is known.

a. What is the final temperature?
b. How much heat is transferred from the left side to the right side?
c. How high is the piston lifted due to the heat transfer?
d. What fraction of the heat is converted to work?

I believe Part b follows directly from the relation between absolute temperature and KE (just find the difference in temperatures between initial and equilibrium states). However, I cannot figure out part a. Any tips/leads would be helpful.

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#### Stovebolt

There are two insulated compartments separated by a thin wall. The left side contains .060 mol of He at a initial temperature of 600 k and the right side contains .030 mol He at the initial temperature of 300 K. The compartment on the right is attached to a vertical cylinder, above which the air pressure is 1.0 atm. A 10-cm-diameter, 2.0 kg piston can slide without friction up and down the cylinder. The volumes of the compartments are not known, but the cylinder diameter is known.

a. What is the final temperature?
b. How much heat is transferred from the left side to the right side?
c. How high is the piston lifted due to the heat transfer?
d. What fraction of the heat is converted to work?

I believe Part b follows directly from the relation between absolute temperature and KE (just find the difference in temperatures between initial and equilibrium states). However, I cannot figure out part a. Any tips/leads would be helpful.
Given that you're only dealing with Helium, the final temperature of the entire system will be equal to the average temperature per mole.

You're on the right track for part b. The energy transferred will be directly proportional to the change in temperature of one side.

One thing to note - while the volume of the compartments are not given, there is enough information to calculate the initial volume of the right compartment. This should help with part c.