One kg of a diatomic gas is at pressure ...

One kg of a diatomic gas is at pressure of `8xx10^4N//m^2`. The density of the gas is `4kg//m^3`. What is the energy of the gas due to its thermal motion?

`5xx10^(4)J`

`6xx10^(4)J`

`7xx10^(4)J`

`3xx10^(4)J`

Text Solution

Verified by Experts

The correct Answer is:

For a diatomic gas, there are 5 degrees of freedom i.e. f = 5.
`therefore` K.E. of the gas due to its thermal motion is given by
`E=f/2RT=f/2PV" ""but"f=5andV=m/rho`
`=5/2xxPxxm/rho`
`=5/2xx8xx10^(4)xx1/4`
`=5xx10^(4)J`

Topper's Solved these Questions

KINETIC THEORY OF GASES ,THERMODYNAMICS AND RADIATION
MARVEL PUBLICATION|Exercise TEST YOUR GRASP - 9|30 Videos
INTERFERENCE AND DIFFRACTION
MARVEL PUBLICATION|Exercise TEST YOUR GRASP|20 Videos
MAGNETIC EFFECTS OF ELECTRIC CURRENT
MARVEL PUBLICATION|Exercise MCQ|195 Videos

Similar Questions

Explore conceptually related problems

Two kg of a monoatomic gas is at a pressure of 4 xx 10^(4) N//m^(2) . The density of the gas is 8 kg//m^(3) . What is the order of energy of the gas due to its thermal motion ?

An ideal gas occupies a volume of 2m^(3) at a pressure of 3xx10^(6) p,a the energy of the gas is :

A closed vessel 10L in volume contains a diatomic gas under a pressure of 10^5N//m^2 . What amount of heat should be imparted to the gas to increase the pressure in the vessel five times?

A balloon inflated with helium gas (density = 0.2 kg//m^(3) ) has a volume of 6 xx 10^(-3) m^(3) . If the density of air is 1.3 kg//m^(3) . What is the buoyant force exerted on the balloon ?

Assertion : A given mass of a gas is subjected to an external pressure of 0.5xx10^(10) N//m^(2) , the bulk modulus of the gas is 0.5xx10^(10) N//m^(2) . The ratio of the density of the gas before and after applying the external pressure is 1 : 1 Reason : Pressure is inversely proportional to density of gas and bulk modulus is inversely proportional to change in volume

One mole of an ideal monoatomic gas occupies a volume of 1.0xx10^-2m^3 at a pressure of 2.0xx10^5N//m^2 . (a) What is the temperature of tha gas? (b) The gas undergoes an adiabatic compression until its volume is decreased to 5.0xx10^-3m^3 . What is the new gas temperature? (c) How much work is done on the gas during the compression? (d) What is the change in the intenal energy of the gas?

For a steel rod, the Young's modulus of elasticity is 2.9xx10^(11)N//m^(2) , and the density of steel is 8xx10^(3)kg//m^(3) .What is the velocity of longitudinal waves in steel?

A gas is compressed from 10 m^3 volume to 4m^3 volume at constant pressure of 50 N//m^(2) . Then the gas is heated by giving it 100 Joules of energy. The internal energy of the gas will

A cylinder contains 12kg of gas at presssure of 10^7 N/ m^2 . The qunatity of gas taken out of the cylinder, if final pressure is 3 Χ 10^6 N/ m^2 , will be (temperature of gas is constant)

12 g of gas occupy a volume of 4xx10^(-3) m^(3) at a temperature of 76^(@)C .after the gas is heated at constant pressure, its density becomes 6xx10^(-4) g//cm^(3) .What is the temperature to which the gas was heated?

MARVEL PUBLICATION-KINETIC THEORY OF GASES ,THERMODYNAMICS AND RADIATION-TEST YOUR GRASP - 9

One kg of a diatomic gas is at pressure of 8xx10^4N//m^2. The density ...
Text Solution
|
The velocities of 4 molecules are 4m/s, 5m/s, 6m/s and 2m/s respective...
Text Solution
|
Oxygen and hydrogen gas are at same temperature and pressure. And the ...
Text Solution
|
The mean free path of nitrogen molecules at 27^(@)C is 3xx10^(-7)m//s....
Text Solution
|
The equation of state for 15 gram of oxygen at pressure P, volume V an...
Text Solution
|
The rms velocity of the molecules of a gas at temperature T is 1200 m/...
Text Solution
|
If atmospheric pressure P=1xx10^(5)N//m^(2)andR=8J//"mole"//""^(@)K, t...
Text Solution
|
At what temperature is the K.E. Of a gas molecules half that of its va...
Text Solution
|
Each molecule of a gas has F degrees of freedom . The ratio (C(p))/(C(...
Text Solution
|
Argon gas is heated at constant volume through 1^(@)C. The heat suppli...
Text Solution
|
C(v) denotes the molar specific heat of a gas at constant volume and g...
Text Solution
|
One mole of a monoatomic ideal gas is mixed with one mole of a diato...
Text Solution
|
Which one of the following is not true about the following thermodynam...
Text Solution
|
During an adiabatic process, the pressure of gas is found to be propor...
Text Solution
|
The difference between the principal specific heats of a gas is 300J/k...
Text Solution
|
When the temperature of 4 moles of a gas was increased from 80^(@)C to...
Text Solution
|
100g of water is heated from 30^@C to 50^@C. Ignoring the slight expan...
Text Solution
|
The temperature of sink of Carnot engine is 27^(@)C. Efficiency of eng...
Text Solution
|
In an ideal refrigerator, heat from inside at 280 K is transferred to ...
Text Solution
|
Which one of the following statements is true in the case of radiation...
Text Solution
|
A perfectly black sphere of diameter 0.2 m is in thermal equilibrium w...
Text Solution
|