Question

A gas undergoes expansion by absorbing 1200J. If 1/4 th of this heat is used in increasing the temperature of the system. Then the work done by the system is:
A. -900J
B. +900J
C. 1500J
D. 300J

Answer 1

Hint: In this question we will use the relation between the work done and the heat absorbed by the gas. Further, by substituting the values, we will get the required result. Further, we will study about the basics of work for our better understanding.

Formula used:
$W = H \times \left( {1 - \dfrac{1}{4}} \right)$

Complete step by step solution:
 As we know that the S.I unit of work is joule is represented J. Joule is defined as the work done by a force of one Newton causing a displacement of one meter. Sometimes, Newton-meter (N-m) is also used for measuring work.
As we know here, heat used to do work W is given as:
$W = H \times \left( {1 - \dfrac{1}{4}} \right)$
Here, H is the heat absorbed by the gas while undergoing expansion.
By substituting the given values in above equation we get:
$\eqalign{
  & \Rightarrow W = - 1200 \times \left( {\dfrac{3}{4}} \right) \cr
  & \therefore W = - 900J \cr} $
Therefore, we get the required result and the correct option is A), i.e., heat used to do the given work is -900J. Here, we have negative signs because the gas is undergoing expansion.

So, the correct answer is “Option A”.

Additional Information: as we know that the work can be defined as the measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement. Further, force experienced by a particle or an object can be defined as the product of mass m and the acceleration a. The S.I. the unit of force is Newton and it is represented as N. The mass of an object is defined as both a property of a physical body and also a measure of its resistance to acceleration or a change in its state of motion, when a net force is applied.
Also it can be said that an object's mass also tells about the strength of its gravitational attraction to other bodies. The SI unit of mass is kilogram or it can be represented as kg.
Pressure applied on an object is defined as the force exerted on the object per unit area.


Note: Here, we should note down that the unit of work can also be given in kilo-Joule, electron volt. From the basic definition of work we can say that when the displacement is zero, which means there is no work done. Also, the heat absorbed in a system which is undergoing expansion is given as a negative sign.