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A Carnot engine operates between two reservoirs of temperatures $900\; \mathrm{K}$ and $300 \;\mathrm{K}$ The engine performs $1200\; \mathrm{J}$ of work per cycle. The heat energy (in $\mathrm{J}$ ) delivered by the engine to the low temperature reservoir, in a cycle. is
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 $1:$ In an adiabatic process, change in internal energy of a gas is equal to work done on/by the gas in the process.
Statement $2 :$ The temperature of a gas remains constant in an adiabatic process.
The pressure $P_{1}$ and density $d_{1}$ of diatomic gas $\left(\gamma=\frac{7}{5}\right)$ changes suddenly to $P _{2}\left(> P _{1}\right)$ and $d _{2}$ respectively during an adiabatic process. The temperature of the gas increases and becomes $......$ times of its initial temperature.$\left(\right.$ given $\left.\frac{ d _{2}}{ d _{1}}=32\right)$
Heat energy of $735\,J$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be $..........\,J$