$A$ gas can be taken from $A$ to $B$ via two different processes $ACB$ and $ADB$. When path $ACB$ is used,$60 \, J$ of heat flows into the system and $30 \, J$ of work is done by the system. If path $ADB$ is used,the work done by the system is $10 \, J$. The heat flow into the system in path $ADB$ is ..... $J$.

First law of thermodynamics is represented by

The first law of thermodynamics is concerned with the conservation of

$A$ cylinder with a piston of unit cross-sectional area contains one mole of an ideal gas as shown in the figure. $A$ spring of unstretched length $L$ and spring constant $K$ is connected between the piston and the bottom of the cylinder. Initially, the spring is unstretched and the gas is in equilibrium. When an amount of heat $Q$ is supplied to the gas, its volume changes from $V_0$ to $V_1$. Find:
$(a)$ The initial pressure of the system.
$(b)$ The final pressure of the system.
$(c)$ Using the first law of thermodynamics, find the relation between $Q, V_0, V_1, P_a$ and $K$.

The volume of one mole of the gas is changed from $V$ to $2V$ at constant pressure $p$. If $\gamma$ is the ratio of specific heats of the gas,what is the change in internal energy of the gas?

An electric heater supplies heat to a system at a rate of $100\;W.$ If the system performs work at a rate of $75\;J/s,$ at what rate (in $J/s$) is the internal energy increasing?