Question 286: Thermodynamics & KTG

Question

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)

Accepted Answer

Let there be n moles of gas
E
loss
= E
gain
$${1 \over 2}(nM){v^2} = n{C_v}\Delta T$$
$${1 \over 2}M{v^2} = {C_v}\Delta T$$
here, $$\gamma  = 1.4 = {7 \over 5}$$ i.e. diatomic gas
$$	herefore$$ $${C_v} = {{5R} \over 2}$$
Now, $${1 \over 2}M{v^2} = {{5R} \over 2}\Delta T$$
$$\Delta T = {{M{v^2}} \over {5R}}$$

Answer

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

Answer

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

Answer

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

Answer

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

Thermodynamics & KTG

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)

Choose the correct answer: