What is the essential difference between microwaves and blue light?.
1 answer:
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Answer:
Speed of the spacecraft right before the collision: .
Assumption: the earth is exactly spherical with a uniform density.
Explanation:
This question could be solved using the conservation of energy.
The mechanical energy of this spacecraft is the sum of:
- the kinetic energy of this spacecraft, and
- the (gravitational) potential energy of this spacecraft.
Let denote the mass of this spacecraft. At a distance of
from the center of the earth (with mass
), the gravitational potential energy (
) of this spacecraft would be:
.
Initially, (the denominator of this fraction) is infinitely large. Therefore, the initial value of
will be infinitely close to zero.
On the other hand, the question states that the initial kinetic energy () of this spacecraft is also zero. Therefore, the initial mechanical energy of this spacecraft would be zero.
Right before the collision, the spacecraft would be very close to the surface of the earth. The distance between the spacecraft and the center of the earth would be approximately equal to
, the radius of the earth.
The of the spacecraft at that moment would be:
.
Subtract this value from zero to find the loss in the of this spacecraft:
Assume that gravitational pull is the only force on the spacecraft. The size of the loss in the of this spacecraft would be equal to the size of the gain in its
.
Therefore, right before collision, the of this spacecraft would be:
.
On the other hand, let denote the speed of this spacecraft. The following equation that relates
and
to
:
.
Rearrange this equation to find an equation for :
.
It is already found that right before the collision, . Make use of this equation to find
at that moment:
.
Answer:
I)
II)The difference from the value obtained on part I is: 2000-1385.67 =614.33
The possible reason of this difference is that the vibrational motion can increase the value, since if we take in count this factor we will have a higher heat capacity, because molecules with vibrational motion require more heat to vibrate and necessary higher specific heat capacity.
Explanation:
From the problem we have the molar mass given of water vapor and at constant volume condition. It's important to say that the vapour molecules have 3 transitionsl and 3 rotational degrees of freedom and the rotational motion no contribution.
Part I
Calculate the specific heat at constant volume of water vapor, assuming the nonlinear triatomic molecule has three translational and three rotational degrees of freedom and that vibrational motion does not contribute. The molar mass of water is 18.0 g/mol=0.018kg/mol.
Let the molar heat capacity at constant volume and this amount represent the quantity of heat absorbed by mole.
Let the specific heat capcity this value represent the heat capacity aboserbed by mass.
For the problem we have a total of 6 degrees of freedom and from the thoery we know that for each degree of freedom the molar heat capacity at constant volume is given by so the total for the 6 degrees of freedom would be:
And by definition we know that the specific heat capacity is defined:
If we replace all the values we have:
So on this case the specific heat capacity with constant volume and with three translational and three rotational degrees of freedom is
Part II
The actual specific heat of water vapor at low pressures is about 2000 J/(kg * K). Compare this with your calculation.
The difference from the value obtained on part I is: 2000-1385.67 =614.33
The possible reason of this difference is that the vibrational motion can increase the value, since if we take in count this factor we will have a higher heat capacity, because molecules with vibrational motion require more heat to vibrate and necessary higher specific heat capacity.