$A$ Carnot engine absorbs $1000\,J$ of heat energy from a reservoir at $127\,^oC$ and rejects $600\,J$ of heat energy during each cycle. The efficiency of the engine and the temperature of the sink will be:

$A$ Carnot engine operates between a source and a sink. The efficiency of the engine is $40 \%$ and the temperature of the sink is $27^{\circ} C$. If the efficiency is to be increased to $50 \%$,then the temperature of the source must be increased by: (in $K$)

$A$ diatomic ideal gas is used as the working substance in a Carnot engine. During the adiabatic expansion process,if the volume of the gas increases from $V$ to $32V$,what is the efficiency of the engine?

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1 :$ An inventor claims to have constructed an engine that has an efficiency of $30\%$ when operated between the boiling and freezing points of water. This is not possible.
Statement $2:$ The efficiency of a real engine is always less than the efficiency of a Carnot engine operating between the same two temperatures.

$A$ Carnot engine working between $300\,K$ and $600\,K$ has a work output of $800\,J$ per cycle. What is the amount of heat energy supplied to the engine from the source per cycle in $J/cycle$?

What is the source temperature of the Carnot engine required to get $70 \%$ efficiency (in $^{\circ}C$)? Given sink temperature $= 27^{\circ}C$.