A large research balloon containing 2.00 × 10^3 m^3 of helium gas at 1.00 atm and a temperature of 15.0°C rises rapidly from ground level to an altitude at which the atmospheric pressure is only 0.900 atm. Assume the helium behaves like an ideal gas and the balloon’s ascent is too rapid to permit much heat exchange with the surrounding air. Required:
a. Calculate the volume of the gas at the higher altitude.
b. Calculate the temperature of the gas at the higher altitude.
c. What is the change in internal energy of the helium as the balloon rises to the higher altitude?

a

b

c

Explanation:

From the question we are told that

  The  volume of the balloon is  

   The  pressure of  helium is  

   The  initial  temperature is  

   The  pressure of  atmosphere is

 Generally the equation representing the  adiabatic process is mathematically represented as

=>    

Generally is a constant with value for an ideal  gas

So  

=>      

Generally the adiabatic process can also be mathematically represented as

=>  

=>    

Generally the ideal gas equation is mathematically represented as

Here  R is the  gas constant with value  

=>  

=>  

Generally change in internal energy i mathematically represented  

Here   is  the  specific heats of gas at constant volume and the value is  

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.