For an ideal gas, the density of the gas is $\rho_0$ when temperature and pressure of the gas are $\mathrm{T}_0$ and $P_0$ respectively. when the temperature of the gas is $2 \mathrm{~T}_0$, its pressure becomes $3 \mathrm{P}_0$. The new density will be

A centigrade and Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit temperature observed is $140^{\circ} \mathrm{F}$. At that time the temperature registered by the centigrade thermometer is

An engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{5}$. When $T_2$ is lowered by 45 K , its efficiency becomes $\frac{1}{2}$. Temperatures $T_1$ and $T_2$ are respectively

Two cylinders A and B fitted with pistons contain equal amount of an ideal rigid diatomic gas at 303 K . The piston of cylinder $A$ is free to move and that of cylinder B is held fixed. The same amount heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder B is 49 K , then the rise in temperature of the gas in $A$ is