$A$ 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...... $kJ$.

During a thermodynamic process,the pressure of a fixed mass of gas is changed in such a way that the gas releases $20 \ J$ of heat and $10 \ J$ of work is done on the gas. If the initial internal energy of the gas is $40 \ J$,then the final internal energy is ...... $J$.

State the first law of thermodynamics and write its limitations.

When $150 \ J$ of heat is supplied to a system,the work done by the system is $110 \ J$. The change in the internal energy of the system is ....... $J$.

$A$ thermodynamic system absorbs $2 \, kcal$ of heat and performs $500 \, J$ of work. The change in its internal energy is ......... $J$.

Consider one mole of perfect gas in a cylinder of unit cross-section with a piston attached as shown in the figure. $A$ spring (spring constant $k$) is attached (unstretched length $L$) to the piston and to the bottom of the cylinder. Initially,the spring is unstretched and the gas is in equilibrium. $A$ certain amount of heat $Q$ is supplied to the gas,causing an increase in volume from $V_0$ to $V_1$.
$(a)$ What is the initial pressure of the system?
$(b)$ What is the final pressure of the system?
$(c)$ Using the first law of thermodynamics,write down a relation between $Q, V_0, V_1, P_a$ and $k$.