Question

A Carnot's engine working between $400\text{K}$ and $800\text{K}$ has a work output of $1200\text{J}$ per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :

• A. $1900\text{J}$
• B. $3200\text{J}$
• C. $2400\text{J}$
• D. $1600\text{J}$

Answer 1

The correct option is C $2400\text{J}$

Efficiency,
$\eta =1-\frac{T_2}{T_1}=\frac{W}{Q_1}$

$T_1=$ Source's temperature $=800\text{K}$
$T_2=$ Sink's temperature $=400\text{K}$
$\eta =$ Efficiency of engine

$W=$ Work output $=1200\text{J}$
$Q_1=$ Heat supplied to engine

So,
$\eta =1-\frac{400}{800}=0.5$

$\Rightarrow 0.5=\frac{W}{Q_1}=\frac{1200}{Q_1}$

$\Rightarrow Q_1=2400\text{J}$