Law A piston with diameter 1-cm and a frictionless plunger is filled with a diat
ID: 1719101 • Letter: L
Question
Law A piston with diameter 1-cm and a frictionless plunger is filled with a diatomic ideal gas. The piston is connected to a gas reservoir ("copper ball"), which is immersed in water, which in turn may be heated. On the diagram, use arrows to indicate all the forces acting on the plunger. Assuming the piston has a diameter of 1 cm, estimate the external force acting on the piston. As we increase the temperature of the gas in the copper ball from Tt to Tz, the piston moves outward, but very slowly. What can you conclude about the pressure of the gas inside the piston (and hence, inside the ball)? Make qualitative sketches of P vs. V and P vs. T and V vs. T for this process. Use the ideal gas law to write an equation for the volume of gas in the piston as a function of the temperature, atmospheric pressure, the volume of the ball and the total number N of molecules in the piston and ball (neglect the connecting tubing), and Boltzmann's constant k_B.Explanation / Answer
>> As, Ideal Gaas Equation is :
PV = NRT
P = Pressure ,
V = Volume
N = No of Moles
R = Gas Constant = k*Na,
k = Boltzmann Constant
Na = Avogadro Number
T = Temperature
>> Now, for Ball,
P*Vb = Nb*RT
>> For Piston, P*Vp = Np*RT
>> Addong Both,
=> P(Vp + Vb) = (Np + Nb)*RT = NRT
=> Vp = Volume of Gas in Piston = NRT/P - Vb
=> Vp = N*k*Na/T/P - Vb
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