Question

600J of heat energy are transferred to a system that does 300J of work.By how much does the system's thermal energy change? Express your answer using two significant figures.

Eth =.....................J

Answer 1

Concepts and reason

The concept required to solve the given problem is first law of thermodynamics.

Determine the mathematical form of first law of thermodynamics and rearrange the expression thus obtained to compute the value of change in internal energy.

Fundamentals

According to first law of thermodynamics, the total energy of an isolated system is constant. In other words the law can also be stated as, “the energy can be transformed from one form to another, but can be neither created nor destroyed.”

According to first law of thermodynamics, the amount of heat Q transferred to a system is equal to the sum of change in internal energy $dU$and work done W by the system. The mathematical form of first law of thermodynamics is,

$Q = dU + W$

According to the first law of thermodynamics, the mathematical expression for heat energy transformed to the system is,

$Q = dU + W$

Rearrange the above equation for change in internal energy $dU.$

$dU = Q - W$

Substitute $600{\rm{ J}}$ for $Q$ and $300{\rm{ J}}$ for $W$ in the above equation $dU = Q - W$and solve for $dU.$

$\begin{array}{c}\\dU = Q - W\\\\ = \left( {600{\rm{ J}}} \right) - \left( {300{\rm{ J}}} \right)\\\\ = 300{\rm{ J}}\\\end{array}$

Ans:

The change in thermal energy of the system is 300 J.