A closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200\, K$. If $0.05$ mole of the same gas at $400\, K$ is added to it, the final  equilibrium temperature (in $K$ ) of the gas in the vessel will be closed to

$Assertion :$ The heat supplied to a system is always equal to the increase in its internal energy.
$Reason :$ When a system changes from one thermal equilibrium to another, some heat is absorbed by it.

In the $P-V$ diagram shown, the gas does $5\, J$ of work in isothermal process $ab$ and $4\,J$ in adiabatic process $bc$.   …. $J$ will be the change in internal energy of the gas in straight path $c$ to $a$ ?

A shown in the figure, the amount of heat absorbed along the path $ABC$ is $90\,J$ and the amount of work done by the system is $30\,J$ . If the amount of work done along the path $ADC$ is $20\,J$ , the amount of heat absorbed will be  …. $J$

$1\, mole$ of an ideal monoatomic gas at temperature $'T_0'$ expands slowly according to the law $P = KV$, where $K$ is a constant. If the final temperature of the gas is $2T_0$. Find the heat supplied to the gas