Question

A perfect gas goes from state A to another state B by absorbing \[8\times {{10}^{5}}J\] of heat and doing $6.5\times {{10}^{5}}J$ of external work. It is now transferred between the same two states in another process in which it absorbs ${{10}^{5}}J$ of heat. In the second process.
 A) Work done on gas is ${{10}^{5}}J$
 B) Work done on gas is $0.5\times {{10}^{5}}J$
 C) Work done by gas is ${{10}^{5}}J$
 D) Work done by gas is $0.5\times {{10}^{5}}J$

Answer 1

Hint: This problem is solved by using the first law of thermodynamics. Heat is a form of energy. As a result of temperature difference heat energy is transferred from one body to another body .Heat flows from hotter body to cooler body. Temperature is the measure of the amount of heat energy present in a body.

Complete step-by-step solution:
Heat transfer is a branch of thermal engineering in that we are going to study the generation of heat transfer and conversion. Heat transfer is the flow of heat due a temperature difference between the bodies.
Heat is a form of energy. Energy is the capacity to do the work and energy exists in different forms.
First law of thermodynamics states that energy can neither be created nor be distorted but it can be transformed to another form.
First law of thermodynamic is formulated as below:
\[\Delta U=Q-W\]
Where$\Delta U$= change in the internal energy of a system
               W=amount of thermodynamic work done by the system
                  Q= quantity of energy supplied to the system as heat
From the data in the first process $Q=8\times {{10}^{5}}J$ and $W=6.5\times {{10}^{5}}J$
$\begin{align}
  & \Delta U=8\times {{10}^{5}}-6.5\times {{10}^{5}} \\
 & \Delta U=1.5\times {{10}^{5}} \\
\end{align}$
In the second process the change in the internal energy of the system remains the same
From the data $Q={{10}^{5}}J$
$W=Q-\Delta U$
$\begin{align}
  & W=1\times {{10}^{5}}-1.5\times {{10}^{5}} \\
 & W=-0.5\times {{10}^{5}}J \\
\end{align}$
Where a negative sign implies that work is done on the gas.
So the correct option is B.

Note: Students Steady state is a situation at which all the state variables are constant and thermal conductivity is usually measured in watts per meter-kelvin. Conservation of energy principle is also called the first law of thermodynamics and energy is a scalar quantity which has only magnitude. SI unit of energy is joule (J).