Question 985: Thermodynamics & KTG

Question

One mole of an ideal gas at an initial temperature of T K does 6R joule of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, the final temperature of gas will be

Accepted Answer

$${T_1} = T,W = 6R\,joules,\gamma  = {5 \over 3}$$
$$W = {{{P_1}{V_1} - {P_2}{V_2}} \over {\gamma  - 1}} = {{nR{T_1} - nR{T_2}} \over {\gamma  - 1}}$$
$$ = {{nR\left( {{T_1} - {T_2}} \right)} \over {\gamma  - 1}}$$
$$n = 1,{T_1} = T \Rightarrow {{R\left( {T - {T_2}} \right)} \over {5/3 - 1}} = 6R$$
$$ \Rightarrow {T_2} = \left( {T - 4} \right)K$$

Answer

(T + 2.4) K

Answer

(T $$-$$ 2.4) K

Answer

(T + 4) K

Answer

(T $$-$$ 4) K

Thermodynamics & KTG

One mole of an ideal gas at an initial temperature of T K does 6R joule of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, the final temperature of gas will be

Choose the correct answer: