Question

(a) Compute the increase in gravitational potential energy for a nitrogen molecule (molar mass ) for an increase in elevation of 400 m near the earth’s surface. (b) At what temperature is this equal to the average kinetic energy of a nitrogen molecule? (c) Is it possible that a nitrogen molecule near sea level where could rise to an altitude of ? Is it likely that it could do so without hitting any other molecules along the way? Explain

Short answer

(A)The temperature of the nitrogen molecule when the gravitational potential energy equal the kinetic energy Is

(B)The increase in gravitational potential energy for an increase in elevation Is .

(C)For the first question the answer will be yes and for the second question the answer will be no

Step-by-step solution

Determine formula for Potential energy and kinetic energy

The gravitational potential energy of an object is defined as the energy possessed by an object rose to a certain height against gravity.

.............Equation 1

Kinetic energy is a property of a moving object or particle and depends not only on its motion but also on itsmass.

..............equation 2

:Determine the increase in gravitational potential energy for an increase in elevation

Solve for Gravitational potential energy from equation 1

substitute in place of m

Therefore ,the increase in gravitational potential energy for an increase in elevation Is .

Given that gravitational potential energy equal to average kinetic energy of the nitrogen

Solve for Temperature of nitrogen molecule from equation 2

Therefore the temperature of the nitrogen molecule when the gravitational potential energy equal the kinetic energy Is .

Determine the possibility that a nitrogen molecule near sea level where  could rise to an altitude of.

For the first question the answer will be yes ,it is possible .Because as the temperature increases kinetic energy increases and it would be larger than the gravitational potential energy so the molecule can rise to an altitude of 400m.

But for the second question the answer will be no ,it's not possible Because as molecules rise there will be many collisions due to increase in temperature and decrease in pressure as it goes high .

Therefore for the first question the answer will be yes and for the second question the answer will be no.