4. One mole of helium gas is injected into each side of a slidable, airtight lead piston that separates two chambers of a sealed cylinder. The outside of the cylinder is insulated everywhere except where noted below. The cylinder and piston have lengths and cross- sectional area labeled in the diagram. The helium in the left chamber is heated from outside at a rate of 450 W, and the helium in the other chamber expels heat into a cool region. The full system eventually comes to steady-state. When it reaches steady state, the force needed to hold on the end cap is measured to be 18,000 N, and the piston has slid to an equilibrium point that is a distance x from the left end. force holding cap = 18,000N pressure. cross-sectional area of cylinder = 0.02m² x = ? Imol He b. Find the distance x. dQ dt =+450W 45cm 15cm lead piston a. Find the temperature difference of the two chambers. Assume helium behaves as an ideal gas, and that heat transfer through the container walls is instantaneous (but not through the lead piston). The thermal conductivity of lead is 35 W/m-K. The force holding the cap accounts for all forces on it, including atmospheric dQ dt c. Find the temperature of the lead piston at its center. 1mol He =-450W

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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4. One mole of helium gas is injected into each side of a slidable, airtight lead piston
that separates two chambers of a sealed cylinder. The outside of the cylinder is insulated
everywhere except where noted below. The cylinder and piston have lengths and cross-
sectional area labeled in the diagram. The helium in the left chamber is heated from outside
at a rate of 450 W, and the helium in the other chamber expels heat into a cool region. The
full system eventually comes to steady-state. When it reaches steady state, the force needed
to hold on the end cap is measured to be 18,000 N, and the piston has slid to an equilibrium
point that is a distance à from the left end.
force holding
cap = 18,000N
pressure.
cross-sectional
area of cylinder
= 0.02m²
x = ?
Imol He
do
dt
= +450W
45cm
15cm
lead piston
a. Find the temperature difference of the two chambers.
b. Find the distance x.
dQ
dt
Assume helium behaves as an ideal gas, and that heat transfer through the container walls
is instantaneous (but not through the lead piston). The thermal conductivity of lead is
35 W/m-K. The force holding the cap accounts for all forces on it, including atmospheric
c. Find the temperature of the lead piston at its center.
Imol He
=-450W
Transcribed Image Text:4. One mole of helium gas is injected into each side of a slidable, airtight lead piston that separates two chambers of a sealed cylinder. The outside of the cylinder is insulated everywhere except where noted below. The cylinder and piston have lengths and cross- sectional area labeled in the diagram. The helium in the left chamber is heated from outside at a rate of 450 W, and the helium in the other chamber expels heat into a cool region. The full system eventually comes to steady-state. When it reaches steady state, the force needed to hold on the end cap is measured to be 18,000 N, and the piston has slid to an equilibrium point that is a distance à from the left end. force holding cap = 18,000N pressure. cross-sectional area of cylinder = 0.02m² x = ? Imol He do dt = +450W 45cm 15cm lead piston a. Find the temperature difference of the two chambers. b. Find the distance x. dQ dt Assume helium behaves as an ideal gas, and that heat transfer through the container walls is instantaneous (but not through the lead piston). The thermal conductivity of lead is 35 W/m-K. The force holding the cap accounts for all forces on it, including atmospheric c. Find the temperature of the lead piston at its center. Imol He =-450W
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