Question

Internal energy of a system increases by $60\,J$ when $140\,J$ of heat is added to the gaseous system. The amount of work done would be:

Answer 1

The energy found within a thermodynamic system is known as its internal energy. It's the amount of energy it takes to construct or prepare a system in any internal state.The first law of thermodynamics is used to understand the relationship between heat, work, and internal energy.

Complete step by step answer:
Remember that energy cannot be produced or destroyed, but it can be transformed from one form to another, according to the theory of conservation of energy. The change in internal energy of a closed system equals the net heat transfer into the system minus the net work performed by the system, according to the first law of thermodynamics. It can be written as,
$\Delta U = Q - W$
Where $\Delta U$ is the change in the system's $\left( U \right)$ internal energy, the total heat movement into and out of the system is denoted by $Q$ and $W$ denotes the system's network.

Notice that we must use the equation $\Delta U = Q + W$ , where W denotes the amount of work performed on the device. In differential form, $du = dq - dw$ , where $dq$ is the differential increment of heat applied to the system, $dw$ is the differential element of work performed by the system, and $du$ is the differential increase in the system's internal energy.

Given that, $du = 60J$ and $dq = 140J$ .
We have to use the formula, $du = dq + dw$
By rearranging the formula,
we get $dw = dq - du$
Then substitute the values,
$\therefore dw = 140\,J - 60\,J = 80\,J$

Hence,The amount of work done would be 80 J.

Note: Internal energy is a broad property that cannot be directly measured. Transfers of matter or energy as heat, as well as thermodynamic function, are the thermodynamic processes that characterise internal energy.The conservation of energy theory is applied to systems that move energy into and out of them using heat and work by the first law of thermodynamics. It can also be used to explain how heat energy is transformed and then transferred again via work.