A vertical cylinder with a heavy piston contains air at 300 K. The initial pressure is 2.0 x 105 Pa and the initial volume is 0.
35 m3 . Take the molar mass of air as 28.9 g/mol and assume Cv= 5 2R. (A) Find the specific heat of air at constant volume in units of J kg·K . (5 pts) (B) Calculate the mass of air in the cylinder. (5 pts) (C) Suppose the piston is fixed. Find the energy input required to raise the temperature to 700 K. (5 pts). (D) Assume again the conditions of the initial state and assume the piston is free to move. Find the energy input to raise the temperature to 700 K. (10 pts)
1 answer:
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Explanation:
Since, the rod is present in vertical position and the spring is unrestrained.
So, initial potential energy stored in the spring is = 0
And, initial potential gravitational potential energy of the rod is .
It is given that,
mass of the bar = 0.795 kg
g = 9.8
L = length of the rod = 0.2 m
Initial total energy T =
Now, when the rod is in horizontal position then final total energy will be as follows.
T =
where, I = moment of inertia of the rod about the end =
Also,
where, = speed of the tip of the rod
x = spring extension
The initial unstrained length is = 0.1 m
Therefore, final length will be calculated as follows.
x' = m
Then, x =
x = m - 0.1 m
= 0.1236 m
k = 25 N/m
So, according to the law of conservation of energy
Putting the given values into the above formula as follows.
v = 2.079 m/s
Thus, we can conclude that tangential speed with which end A strikes the horizontal surface is 2.079 m/s.