Is it possible to increase the temperature of a gas without adding heat to it? Explain.

(A) Yes,during adiabatic compression,the temperature of a gas increases even though no heat is added to it.
In an adiabatic process,the heat exchange $\Delta Q = 0$.
According to the first law of thermodynamics:
$\Delta Q = dU + dW$
Since $\Delta Q = 0$,we have $0 = dU + dW$,which implies $dU = -dW$.
During compression,work is done on the gas,so the work done $dW$ is negative $(dW < 0)$.
Substituting this into the equation: $dU = -(-|dW|) = |dW|$.
Since $dU > 0$,the internal energy of the gas increases.
Because the internal energy $U$ of an ideal gas is directly proportional to its absolute temperature $(U \propto T)$,an increase in internal energy results in an increase in the temperature of the gas.