Answer

Verified

429.3k+ views

**Hint:-**The box is insulated which means that no heat will be absorbed from the outside of the box. The change in the kinetic energy of the box will be the reason for increase in the internal energy and also the change in the kinetic energy.

Formula used: The formula of the kinetic energy of a body of mass ‘m’ and velocity ‘v’ is given by,

$K.E = \dfrac{1}{2}m \cdot {v^2}$………eq. (1)

The formula of increase in internal energy of the monatomic gas is given by,

$\Delta E = \dfrac{3}{2}nR\Delta T$………eq. (2)

Where n is the number of moles R is the universal gas constant and $\Delta T$ is the change in temperature.

**Complete step-by-step solution**:It is given that an insulated box containing monatomic ideal gas of molar mass M is moving with a uniform speed v the box suddenly stops and consequently the gas acquires a new temperature and we need to find the change in the temperature of the gas.

The change in the internal energy is equal to the increase in the internal energy of the monatomic gas.

As the final velocity of the box is zero and therefore the final kinetic energy of the box will be zero.

Since the change in the kinetic will be equal to the increase in the internal energy of the monatomic gas in the box.

$ \Rightarrow {\text{K}}{\text{.E}} = {\text{Increase in internal energy }}$

Using equation (1) and equation (2) we get,

$ \Rightarrow \dfrac{1}{2}m \cdot {v^2} = \dfrac{3}{2}nR\Delta T$………eq. (3)

As mole is defined as the ratio of mass of the gas to the molecular mass of the gas so we get,

$n = \dfrac{m}{M}$.

Replace the value of n in the equation (3)

$ \Rightarrow \dfrac{1}{2}m \cdot {v^2} = \dfrac{3}{2}nR\Delta T$

$ \Rightarrow \dfrac{1}{2}m \cdot {v^2} = \dfrac{3}{2}\left( {\dfrac{m}{M}} \right)R\Delta T$

$ \Rightarrow {v^2} = \left( {\dfrac{3}{M}} \right)R\Delta T$

$ \Rightarrow \Delta T = \dfrac{{M \cdot {v^2}}}{{3 \cdot R}}$

The change in the temperature of the gas is equal to$\Delta T = \dfrac{{M \cdot {v^2}}}{{3 \cdot R}}$.

**The correct answer for this problem is option B.**

**Note:-**The final velocity of the box is zero and therefore the value of kinetic energy will be also zero. The change in internal energy of a gas is caused by the striking of the molecules of gas with each other and also with the walls of the container.

Recently Updated Pages

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

10 examples of evaporation in daily life with explanations

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE