Question 309: Thermodynamics & KTG

Question

Two Carnot engines A and B operate in series such that engine A absorbs heat at T
1
and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T
3
. When workdone in both the cases is equal, to value of T is :

Accepted Answer

$${W_A} = 1 - {{{Q_2}} \over {{Q_1}}} = 1 - {T \over {{T_1}}} \Rightarrow {{{Q_2}} \over {{Q_1}}} = {T \over {{T_1}}}$$
$${W_B} = 1 - {{{Q_3}} \over {({Q_2}/2)}} = 1 - {{{T_3}} \over T} \Rightarrow {{2{Q_3}} \over {{Q_2}}} = {{{T_3}} \over T}$$
Now, W
A
= W
B
$${Q_1} - {Q_2} = {{{Q_2}} \over 2} - {Q_3}$$
$$ \Rightarrow {{2{Q_1}} \over {{Q_2}}} + {{2{Q_3}} \over {{Q_2}}} = 3$$
$$ \Rightarrow {{2{T_1}} \over T} + {{{T_3}} \over T} = 3$$
$$ \Rightarrow $$ $${{2{T_1}} \over 3} + {{{T_3}} \over 3} = T$$

Answer

$${2 \over 3}{T_1} + {3 \over 2}{T_3}$$

Answer

$${1 \over 3}{T_1} + {2 \over 3}{T_3}$$

Answer

$${3 \over 2}{T_1} + {1 \over 3}{T_3}$$

Answer

$${2 \over 3}{T_1} + {1 \over 3}{T_3}$$

Thermodynamics & KTG

Two Carnot engines A and B operate in series such that engine A absorbs heat at T 1 and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T 3 . When workdone in both the cases is equal, to value of T is :

Choose the correct answer: