JEE MAIN - Physics (2022 - 26th June Morning Shift - No. 8)

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by :

(R = universal gas constant)

$${{M{v^2}} \over {7R}}$$
$${{M{v^2}} \over {5R}}$$
2$${{M{v^2}} \over {7R}}$$
7$${{M{v^2}} \over {5R}}$$

Explanation

Let there be n moles of gas

Eloss = Egain

$${1 \over 2}(nM){v^2} = n{C_v}\Delta T$$

$${1 \over 2}M{v^2} = {C_v}\Delta T$$

here, $$\gamma = 1.4 = {7 \over 5}$$ i.e. diatomic gas

$$\therefore$$ $${C_v} = {{5R} \over 2}$$

Now, $${1 \over 2}M{v^2} = {{5R} \over 2}\Delta T$$

$$\Delta T = {{M{v^2}} \over {5R}}$$

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