Answer:
T=C*P*V
Explanation:
It is said that a variable - let's call 'y' -, is proportional to another - let's call it 'x' - if x and y are multiplicatively connected to a constant 'C'. It means that their product (x*y) can be always equaled to the constant 'C' or their division (
) can be always equaled to 'C'. The first case is the case of the inverse proportionality: It is said that x and y are inversely proportional if
The second case is the case of the direct proportionality: It is said that x and y are directly proportional if
: x is directly proportional to y.
or
: y is directly proportional to x.
Always that any text does not specify about directly or inversely proportionality, it is assumed to mean directly automatically.
For our case, we are said that the temperature T is proportional to the pressure P and the volume V (we assume that it means directly); it is a double proportionality but follows the same rules:
If T were just proportional to P, we would have:
If T were just proportional to V, we would have:
As T is proportional to both P and V, the right equation is:
In order to isolate the temperature, let's multiply (P*V) at each side of the equation:
In the circular motion of the hammer, the centripetal force is given by
where m is the mass of the hammer, v its tangential speed and r is the distance from the center of the motion, i.e. the length of the hammer.
Using the data of the problem, we find:
Anything that's not supported and doesn't hit anything, and
doesn't have any air resistance, gains 9.8 m/s of downward
speed every second, on account of gravity. If it happens to
be moving up, then it loses 9.8 m/s of its upward speed every
second, on account of gravity.
(64.2 m/s) - [ (9.8 m/s² ) x (1.5 sec) ]
= (64.2 m/s) - [ 14.7 m/s ]
= 49.5 m/s . (upward)
Answer:
U = 12,205.5 J
Explanation:
In order to calculate the internal energy of an ideal gas, you take into account the following formula:
(1)
U: internal energy
R: ideal gas constant = 8.135 J(mol.K)
n: number of moles = 10 mol
T: temperature of the gas = 100K
You replace the values of the parameters in the equation (1):
The total internal energy of 10 mol of Oxygen at 100K is 12,205.5 J
Answer:
The amount of work that must be done to compress the gas 11 times less than its initial pressure is 909.091 J
Explanation:
The given variables are
Work done = 550 J
Volume change = V₂ - V₁ = -0.5V₁
Thus the product of pressure and volume change = work done by gas, thus
P × -0.5V₁ = 500 J
Hence -PV₁ = 1000 J
also P₁/V₁ = P₂/V₂ but V₂ = 0.5V₁ Therefore P₁/V₁ = P₂/0.5V₁ or P₁ = 2P₂
Also to compress the gas by a factor of 11 we have
P (V₂ - V₁) = P×(V₁/11 -V₁) = P(11V₁ - V₁)/11 = P×-10V₁/11 = -PV₁×10/11 = 1000 J ×10/11 = 909.091 J of work
