Question 460: Thermodynamics & KTG

Question

A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma .$ It is moving with speed $v$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:

Accepted Answer

Here, work done is zero.
So, loss in kinetic energy $=$ change in internal energy of gas
${1 \over 2}m{v^2} = n{C_v}\Delta T = n{R \over {\gamma  - 1}}\Delta T$
${1 \over 2}m{v^2} = {m \over M}{R \over {\gamma  - 1}}\Delta T$
$	herefore$ $\Delta T = {{M{v^2}\left( {\gamma  - 1} ight)} \over {2R}}K$

Answer

${{\left( {\gamma  - 1} \right)} \over {2\gamma R}}M{v^2}K$

Answer

${{\gamma {M^2}v} \over {2R}}K$

Answer

${{\left( {\gamma  - 1} \right)} \over {2R}}M{v^2}K$

Answer

${{\left( {\gamma  - 1} \right)} \over {2\left( {\gamma  + 1} \right)R}}M{v^2}K$

Thermodynamics & KTG

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats \gamma . It is moving with speed v and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:

Choose the correct answer: