Question

V varies inversely with T and $V=18$ when $T=3$. Then write the relation between V and T?

Answer 1

Hint: We have given that V varies inversely with T so the relation between V and T is as follows: $V=\dfrac{a}{T}$. Now, in this equation, “a” is the constant and “V and T” are the variables so we are going to find this value of constant “a” by substituting the value of V and T which is equal to: $V=18,T=3$. After that, we will solve this relation and will get the value of constant “a”.

Complete step by step solution:
In the above problem, it is given that V varies inversely with T so the relation between V and T is as follows:
$V=\dfrac{a}{T}$ ………… (1)
In the above equation, “a” is constant. Also, it has been asked in the problem that we have to write the relation between V and T. For this equation, we are going to substitute the value of V and T given in the above problem i.e. $\left( V=18,T=3 \right)$.
$\Rightarrow 18=\dfrac{a}{3}$
Multiplying 3 on both the sides we get,
$\begin{align}
  & \Rightarrow 18\times 3=a \\
 & \Rightarrow 54=a \\
\end{align}$
From the above, we have found the value of “a” and now, substituting this value of “a” in eq. (1) we get,
$\Rightarrow V=\dfrac{54}{T}$
Hence, the required equation is $V=\dfrac{54}{T}$.

Note: You can check the relation which we derived above is correct or not by substituting the values of V and T given above and see whether the equation holds true or not.
The equation which we have solved in the above problem is as follows:
$\Rightarrow V=\dfrac{54}{T}$
Substituting the values of V and T as $\left( V=18,T=3 \right)$ in the above equation and we get,
$\Rightarrow 18=\dfrac{54}{3}$
On cross multiplying the above equation we get,
$\begin{align}
  & \Rightarrow 18\times 3=54 \\
 & \Rightarrow 54=54 \\
\end{align}$
As you can see that L.H.S = R.H.S so the equation which we have solved above is correct.