- #1

LCSphysicist

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- Homework Statement
- A thin-walled metal container of volume V contains a gas at high pressure.

Connected to the container is a capillary tube and stopcock. When the stopcock is

opened slightly, the gas leaks slowly into a cylinder equipped with a nonleaking,

frictionless piston, where the pressure remains constant at the atmospheric value $P_0$.

(a) Show that, after as much gas as possible has leaked out, an amount of work $P_0(V_0-V)$

has been done, where $V_0$ is the volume of the gas at atmospheric pressure and

temperature.

(b) How much work would be done if the gas leaked directly into the atmosphere?

- Relevant Equations
- .

I will summarize briefly my reasoning for both letters, since the answer is immediately after that:

A) The work is quasi-static, and the pressure is approximatelly constant and equal to the atmospheric pressure, so the works is $$W = -p\int dV = -p_{0} (V_{0}-V)$$

B) The work is fast, fast enough that no heat flows thought the gas, so that the work is $$W = -\int p dV = -\int_{V_i}^{V_f} p_i (V_i)^{\gamma} dV /V^{\gamma}$$ $$ P_i V_i^{\gamma} / P_o = V_f ^{\gamma}$$

What do you think? I am almost sure it is wrong, so i am posting here to get any help on letter b

A) The work is quasi-static, and the pressure is approximatelly constant and equal to the atmospheric pressure, so the works is $$W = -p\int dV = -p_{0} (V_{0}-V)$$

B) The work is fast, fast enough that no heat flows thought the gas, so that the work is $$W = -\int p dV = -\int_{V_i}^{V_f} p_i (V_i)^{\gamma} dV /V^{\gamma}$$ $$ P_i V_i^{\gamma} / P_o = V_f ^{\gamma}$$

What do you think? I am almost sure it is wrong, so i am posting here to get any help on letter b