Question

A cylinder of fixed capacity $67.2$ liters contains helium gas at STP . Calculate the amount of heat required to rise the temperature of the gas by ${20^o}C$ ?
A) $748J$
B) $374J$
C) $350J$
D) $700J$

Answer 1

Hint: This must be treated in the Standard conditions as it is given that the conditions are STP. Now all the given conditions should be mentioned in the equation and solve accordingly. So first of all we need to sort out all the given conditions for the system then we can apply the equation ${C_v} = (\dfrac{f}{2})R$ to find the specific heat at constant volume, to be used in the equation $\Delta Q = n{C_v}\Delta T$ , and to find the answer.

Complete step by step answer:
First of all we have to get out the quantities which have been mentioned in the given question. They are :The capacity of the cylinder : $67.2$ litres
The gas which is present : Helium
The temperature required to reach : ${20^o}C$
So, we just have to use some of the formulas from the field of thermodynamics in order to derive the relation between the temperature and the heat along with the nature of the gas.
First of all we need to acquire the specific heat at constant volume of gas using the formula : ${C_v} = (\dfrac{f}{2})R$ where the $f$defines the degree of the freedom of the gas.
The equation we have to use here is:
$
 $\implies$ \Delta Q = n{C_v}\Delta T \\
 $\implies$ \Delta Q = n\dfrac{3}{2}\Delta T \\
 $
$\dfrac{3}{2}$ because of the Helium gas being diatomic in nature.
So, further we have to mention all the attributes according to STP:
\[
   = (\dfrac{{67.2}}{{22.4}})*(\dfrac{3}{2}*8.31)*20 \\
   \approx 784J \\
 \]
$\therefore$ The correct option is A.

Note: The specific gas at the constant volume is the gas specific quantity when compared. In simple terms we can say that it varies from gas to gas though have the same for the gases with the same number of the atomicity.