Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

A sample of gas in a box is at pressure P0 and temperatureT0. If number of molecules is doubled and total kinetic energy of the gas kept constant, then final temperature and pressure will be
T0.P0
T0.2P0
T02.2P0
T02.P0

Answer
VerifiedVerified
487.8k+ views
3 likes
like imagedislike image
Hint: Use the formula for kinetic energy of the gas relating number of moles and temperature to find the relation between final and initial temperature. In ideal gas equation, the product of pressure and volume remains constant.

Formula Used: K.E=f2nRT0
Here, f is the degree of freedom, n is the number of moles of the gas, and R is the gas constant.

Complete step by step answer:We aren't given whether the gas is monatomic or diatomic. Therefore, the kinetic energy of the gas at temperature T0 is,
K.E=f2nRT0

Here, f is the degree of freedom, n is the number of moles of the gas, and R is the gas constant.

The kinetic energy of the gas when the number of molecules is doubled is,
K.E=f2(2n)RT1

Here, T1 is temperature of the gas when the number of molecules is doubled.

We have given that the kinetic energy of the gas is constant, therefore, we can write,
f2(2n)RT1=f2nRT0
T1=T02

Therefore, the temperature of the gas will be half of the initial value.

The volume of the box is constant. Therefore, the volume of the gas will not increase in both the cases.

Now, according to the ideal gas equation, PV=nRT, the product PV always remains constant. Since the volume does not change, the pressure also must not change.

Therefore, the final pressure will be P0.

So, the correct answer is option (D).

Note:Students should note that when the number of molecules is doubled, the number of moles also gets doubled. We know that one mole is equal to Avagadro’s number. When the number of moles of the gas increases, the temperature of the gas decreases, keeping the product PV constant.