$A$ system is given $300$ calories of heat and it does $600$ joules of work. How much does the internal energy of the system change in this process? $(1 \text{ calorie} = 4.18 \text{ joules})$

The heat supplied to a gas at a constant pressure of $5 \times 10^5 \ Pa$ is $1000 \ kJ$. If the volume of gas changes from $1 \ m^3$ to $2.5 \ m^3$,then the change in internal energy of the gas is (in $kJ$)

$A$ gas is compressed at a constant pressure of $50 \ N/m^{2}$ from a volume of $10 \ m^{3}$ to $4 \ m^{3}$. Then,the gas is heated by supplying $100 \ J$ of energy. The increase in its internal energy will be ..... $J$.

$A$ system is provided with $200 \, cal$ of heat and the work done by the system on the surroundings is $40 \, J$. Then its internal energy

$A$ system performs work $\Delta W$ when an amount of heat $\Delta Q$ is added to the system. The corresponding change in the internal energy is $\Delta U$. Which of the following is a unique function of the initial and final states (irrespective of the mode of change)?

$A$ thermally insulated rigid container contains an ideal gas heated by a filament of resistance $100 \,\Omega$ through a current of $1 \,A$ for $5 \,min$. The change in internal energy is...... $kJ$.